Rate Of Convergence In Numerical Analysis

Rate Of Convergence In Numerical Analysis In numerical analysis, the speed at which a convergent sequence approaches its limit is called the rate of convergence. Strictly speaking, a limit does not give information about any finite first part of the sequence; this concept is of practical importance if we deal with a sequence of successive approximations for a iterative method, as typically fewer iterations are needed to output a useful approximation if the rate of convergence is higher. This may even make the difference between needing ten or a million iterations. Similar concepts are used for discretization methods. The solution of the discretized problem converges to the solution of the continuous problem as the grid size goes to zero, and the speed of convergence is one of the factors of the efficiency of the method. However, the terminology in this case is different from the terminology for iterative methods. Convergence speed for iterative methods Basic definition Suppose that the sequence {xk} converges to the number L. We say that this sequence converges linearly to L, if there exists a number ÃŽÂ ¼ à ¢Ã‹â€ Ã‹â€  (0, 1) such that The number ÃŽÂ ¼ is called the rate of convergence. If the above holds with ÃŽÂ ¼ = 0, then the sequence is said to converge superlinearly. One says that the sequence converges sublinearly if it converges, but ÃŽÂ ¼=1. The next definition is used to distinguish superlinear rates of convergence. We say that the sequence converges with order q for q > 1 to L if In particular, convergence with order 2 is called quadratic convergence, and convergence with order 3 is called cubic convergence. This is sometimes called Q-linear convergence, Q-quadratic convergence, etc., to distinguish it from the definition below. The Q stands for quotient, because the definition uses the quotient between two successive terms. Extended definition The drawback of the above definitions is that these do not catch some sequences which still converge reasonably fast, but whose speed is variable, such as the sequence {bk} below. Therefore, the definition of rate of convergence is sometimes extended as follows. Under the new definition, the sequence {xk} converges with at least order q if there exists a sequence {ÃŽÂ µk} such that and the sequence {ÃŽÂ µk} converges to zero with order q according to the above simple definition. To distinguish it from that definition, this is sometimes called R-linear convergence, R-quadratic convergence, etc. Examples Consider the following sequences: The sequence {ak} converges linearly to 0 with rate 1/2. More generally, the sequence CÃŽÂ ¼k converges linearly with rate ÃŽÂ ¼ if |ÃŽÂ ¼| CONVERGENCE SPEED FOR DISCRETIZATION METHODS A similar situation exists for discretization methods. Here, the important parameter is not the iteration number k but the number of grid points, here denoted n. In the simplest situation (a uniform one-dimensional grid), the number of grid points is inversely proportional to the grid spacing. In this case, a sequence xn is said to converge to L with order p if there exists a constant C such that | xn à ¢Ã‹â€ Ã¢â‚¬â„¢ L | This is written as |xn L| = O(n-p) using the big O notation. This is the relevant definition when discussing methods for numerical quadrature or the solution of ordinary differential equations. Examples The sequence {dk} with dk = 1 / (k+1) was introduced above. This sequence converges with order 1 according to the convention for discretization methods. The sequence {ak} with ak = 2-k, which was also introduced above, converges with order p for every number p. It is said to converge exponentially using the convention for discretization methods. However, it only converges linearly (that is, with order 1) using the convention for iterative methods. RATE OF CONVERGENCE OF BISECTION METHOD If f is a continuous function on the interval [a, b] and f(a)f(b) The bisection method gives only a range where the root exists, rather than a single estimate for the roots location. Without using any other information, the best estimate for the location of the root is the midpoint of the smallest bracket found. In that case, the absolute error after n steps is at most If either endpoint of the interval is used, then the maximum absolute error is the entire length of the interval. These formulas can be used to determine in advance the number of iterations that the bisection method would need to converge to a root to within a certain tolerance. For, using the second formula for the error, the number of iterations n has to satisfy to ensure that the error is smaller than the tolerance ÃŽÂ µ. If f has several simple roots in the interval [a,b], then the bisection method will find one of them. RATE OF CONVERGENCE OF FALSE-POSITION METHOD If the initial end-points a0 and b0 are chosen such that f(a0) and f(b0) are of the opposite signs, then one of the end-points will converge to a root of f. The other end-point will remain fixed for all subsequent iterations while the converging endpoint becomes updated. Unlike the bisection method, the width of the bracket does not tend to zero. As a consequence, the linear approximation to f(x), which is used to pick the false position, does not improve in its quality. One example of this phenomenon is the function, f(x) = 23 à ¢Ã‹â€ Ã¢â‚¬â„¢ 42 + 3x on the initial bracket [à ¢Ã‹â€ Ã¢â‚¬â„¢1,1]. The left end, à ¢Ã‹â€ Ã¢â‚¬â„¢1, is never replaced and thus the width of the bracket never falls below 1. Hence, the right endpoint approaches 0 at a linear rate. While it is false to think that the method of false position is a good method, it is equally a mistake to think that it is unsalvageable. The failure mode is easy to detect and easily remedied by next picking a modified false position, such as or down-weighting one of the endpoint values to force the next ck to occur on that side of the function. There are other ways to pick the rescaling which give even better convergence rates. RATE OF CONVERGENCE OF SECANT METHOD The iterates xn of the secant method converge to a root of f, if the initial values x0 and x1 are sufficiently close to the root. The order of convergence is ÃŽÂ ±, where is the golden ratio. In particular, the convergence is superlinear. This result only holds under some technical conditions, namely that f be twice continuously differentiable and the root in question be simple (i.e., with multiplicity 1). If the initial values are not close to the root, then there is no guarantee that the secant method converges. The right-most quantity above may be expressed as since . Then, from a Taylor expansion of about one finds for some . Similarly Placing these quantities into Equation 4.9 will result in some cancellation, or The approximation expressed in Equation 4.11 can be explicitly quantified by recognizing that for some . Hence This completes the analysis of the final term in Equation 4.8. The first term in Equation 4.8 can be analyzed similarly, to obtain Hence, the error given in the secant method is roughly given as A more careful investigation and analysis produces the exact expression for some . To generate a complete convergence analysis, assume that f(x) is bounded and in some neighborhood of . These assumptions imply that sufficiently close to . Further, assume that the initial values and are chosen sufficiently close to to satisfy for some K The exponents on K form the Fibonacci sequence, . The Fibonacci sequence is defined inductively, as The general error term is then given to be The Fibonacci number have an explicit formula, namely with . Note that , and since K At this point, we have While somewhat complex-looking, the equation above actually produces the convergence rate that we seek. RATE OF CONVERGENCE OF NEWTON RAPHSON METHOD Suppose that the function Æ’ has a zero at ÃŽÂ ±, i.e., Æ’(ÃŽÂ ±) = 0. If f is continuously differentiable and its derivative is nonzero at ÃŽÂ ±, then there exists a neighbourhood of ÃŽÂ ± such that for all starting values x0 in that neighbourhood, the sequence {xn} will converge to ÃŽÂ ±. If the function is continuously differentiable and its derivative is not 0 at ÃŽÂ ± and it has a second derivative at ÃŽÂ ± then the convergence is quadratic or faster. If the second derivative is not 0 at ÃŽÂ ± then the convergence is merely quadratic. If the third derivative exists and is bounded in a neighbourhood of ÃŽÂ ±, then: where If the derivative is 0 at ÃŽÂ ±, then the convergence is usually only linear. Specifically, if Æ’ is twice continuously differentiable, Æ’ (ÃŽÂ ±) = 0 and Æ’ (ÃŽÂ ±) à ¢Ã¢â‚¬ °Ã‚   0, then there exists a neighbourhood of ÃŽÂ ± such that for all starting values x0 in that neighbourhood, the sequence of iterates converges linearly, with rate log10 2 (Sà ¼li Mayers, Exercise 1.6). Alternatively if Æ’ (ÃŽÂ ±) = 0 and Æ’ (x) à ¢Ã¢â‚¬ °Ã‚   0 for x à ¢Ã¢â‚¬ °Ã‚   0, x in a neighbHYPERLINK http://en.wikipedia.org/wiki/Topological_neighborhoodourhood U of ÃŽÂ ±, ÃŽÂ ± being a zero of multiplicity r, and if Æ’ à ¢Ã‹â€ Ã‹â€  Cr(U) then there exists a neighbourhood of ÃŽÂ ± such that for all starting values x0 in that neighbourhood, the sequence of iterates converges linearly. However, even linear convergence is not guaranteed in pathological situations. In practice these results are local and the neighbourhood of convergence are not known a priori, but there are also some results on global convergence, for instance, given a right neighbourhood U+ of ÃŽÂ ±, if f is twice differentiable in U+ and if , in U+, then, for each x0 in U+ the sequence xk is monotonically decreasing to ÃŽÂ ±. Proof of quadratic convergence for Newtons iterative method According to TaylorHYPERLINK http://en.wikipedia.org/wiki/Taylors_theoremHYPERLINK http://en.wikipedia.org/wiki/Taylors_theorems theorem, any function f(x) which has a continuous second derivative can be represented by an expansion about a point that is close to a root of f(x).

“In Praise of Cultural Imperialism” by David Rothkopf Essay

In the article, In Praise of Cultural Imperialism, David Rothkopf illustrates a progressive new world order where information is the new global currency and the United States, â€Å"the indispensable nation,† is the bank. In his article, Rothkopf contrasts the victimizing tendencies of ‘cultural barriers’, which are the unmistakably causing ethnic, religious, ideological, tribal or nationalistic conflicts, to the uniting tendencies of western globalization. Rothkopf predicts the inevitable merging of all the cultures under the common benefits originating from globalization once â€Å"they have realized that to compete in the global marketplace they must conform to the culture of that marketplace† The United States whose policies are evidently â€Å"the best model for the future† will lead this next step in civilization’s evolution, all the while making sure that â€Å"if common values are being developed, they be the values with which Americans are comfortable.† Rothkopf further states that it is in the US’s best interest â€Å"to encourage the development of a world in which the fault lines separating nations are bridged by shared interest† ultimately leading to a more peaceful and tolerant future: â€Å"Globalization is a vital step toward both a more stable world and better lives for the people in it.† Rothkopf, the former Deputy Undersecretary of the Commerce Department under the Clinton Administration and now the president of an international advisory firm, is also an adjunct professor of international and public affairs at Columbia University. Consequently, his views clearly demonstrate a pro-American capitalist’s stance on the issues pertaining to American economics, cultural imperialism and foreign policy. In his article, Rothkopf describes the power of culture and its influence over this new age global environment, with its power to â€Å"bind and to divide in a time when the tensions between integration and separation tug at every issue that is relevant to international relations.† Moreover, he claims that although critics of globalization may condemn the â€Å"homogenizing influences of globalization,† the effects of globalization are more consistently positive than negative. This is because globalization has an integrating dimension to it. Rothkopf believes that the â€Å"United States is in a position not only to lead in the 21st century as the dominant power of the Information Age, but to do so by breaking down the barriers that divide nations–and groups  within nations–and by building ties that create an ever greater reservoir of shared interests among an ever larger community if peoples† This â€Å"removal not only of cultural barriers but of many of the negative dimensions of culture† could only result in stability†¦right? Rothkopf views could be easily dismissed, as an arrogant fantasy-ridden interpretation of the future. However, although many cultures may not see the benefits of melting themselves into an existence that is in every aspect dominated by western values, the influence of American culture on the rest of the world is evident. Whether this influence will or has been completely positive has yet to be proven. Although Rothkopf believes that globalization is the key to a peaceful future whose culturally uniting fundamentals lie with the United States, he underestimates the complex nature of culture and its strength in relation to globalization. Culture is not something that can be simply defined as Webster’s Third New International Dictionary does, nor will it be easily moulded into a tool to be used for the expansion of American interests. Many cultures around the world, such as in the Muslim block, guard their culture and religion with their lives, for culture and religion are one in the same in Islam. As was illustrated on September 11th, many will even sacrifice their lives for causes they perceive threaten the existence of their culture/religion. Another aspect of globalization that Rothkopf does not develop is the apparent social stratification created by globalization. It is arguable that to sustain globalization, cheap labour must readily available. If undeveloped countries become developed and the poor majority become empowered, where will the cheap labour come from? Although Rothkopf may bring attention to the overbearing extension of American cultural values over the globe, he underestimates how the rest of the worlds’ varied and contrasting cultural values will effect the global environment. Consequently, his extremely biased perspectives undermine some of the more valid points of his article.

Autonomous work group an essential ingredient for effective organising? Essay

Following the needs of many businesses to adopt alternative forms of work design this paper tries to explain and make some sense about the effectiveness of autonomous work groups in organising. It will be argue the thesis that such groups have been, are and will be effective in some definite organisational setting. The assumptions underpinning this idea will be explored along the dialectic forming three sections. To understand this concept it seems important introduce notions of individual, group and explain why they are so central from an organisational point of view. Thus, the first part of this paper will present some psychological effects resulting through their interaction of these actors Moreover, being the idea of autonomous work group part of a complex system, it will be restrictive analyse its characteristics without locate it among others concepts produced by sociotechnical researchers. Thus, a broader analysis of sociotechnical system (STS) will be part of the second section. Difference between what STS aimed to achieve, what they really achieved, and/or what they are achieving today is still discussed. This lack of unanimous consensus lets the debate open to several interpretations, and offer the opportunity to explore and address few issues related to the self-managing groups. Hence, the last side of this paper will address a discuss about the role of management, the subordination of human criteria to the dictates of efficiency, the application to both linear and non-linear systems, and a movement toward a self-leading team type. The magnitude of such topic and the number of interesting studies surrounding this area offer to the author a dilemma regarding what should be treated and what should not. Obviously, having this script humanistic approach major evidence is given to people in organisation, and respectively team members, and management. Moreover, analysing the way in which the system adapted itself during the second half of the last century, it will be argued that organisations designed or redesigned in respect of human criteria in certain industries and environments, can reach a competitive advantage respect those that will not do it. In short, STS is an effective tool by which it is possible match both individual and organisational needs. Pursuing the paper this line of argument, issues related to politics, unions, and power, and other effects of identifications, ideology and control are not dealt in this paper neither because not relevant, nor because of secondary importance, rather, due to the limitation of the length. Individuals, Groups and Organisation To some extent groups always existed, even in USA -where in time of cold war ambitions were led to unbridled individualism, organisation used to split task into subtask, assigned it to various subunits, than these subunits divided subtask into sub-subunits and so on. Even if an organisation is formally organised according individual performance, the division of labour break down the organisation into groups. What does group means, and what needs a group fulfil for both organisation and individual? ‘A psychological group is any number of people who interact with one other, are psychologically aware of one other, and perceive themselves as group’ (Schein 1994), and are seen as group by the others from outside (Hackman 1987, in Brown 2003). If in everyday life, groups can be formed through a spontaneous or random meeting -such as four friends meets for chance in library, in organisational setting they have diverse origin. Basically, it is possible recognise two types of groups in organisation, those which are deliberately created by managers in order to fulfil the tasks required from the organisational mission, an those fulfilling psychological needs of individual beyond the minimum ones of doing their jobs; respectively formal and informal groups (Schein 1994). According to its duration the former can be of two types: permanent -such as the group of lecturer or/and professors forming the BOR depth at Lancaster University; or temporary -such as a matrix group of lecturers or/and professors committed in a project for a definite time or mission. Nevertheless, organisation takes an informal structure within which individuals interacting with others generates a group that fulfil their social needs. But contrary to the everyday life the interaction depend on defined physical location, being in fact their activity within the organisation limited by their tasks and mission to perform -such as the possibility to interact with people both meeting and working in the same office, depth, building and so on. Bearing in mind that groups can simultaneously fulfil diverse organisational functions and needs of their members, it useful here to distinguish these kinds of functions in ‘organisational and individual’ (Schein 1994). According to this partition, it is possible group organisational functions as those features coinciding with the mission of the organisation -i.e. working on a complex or interdependent task, generating new ideas or creative solutions, liaison or coordinating functions, facilitate the implementation of complex decision, or be a vehicle of socialisation or training. On the other hand, among needs group members can bring with them and groups can fulfil there are needs such as those of affiliation, sense of identification and maintain self esteem, establish and tests social reality, moreover, it reduce insecurity and anxiety. Appear now clear why groups are so important, from an organisational point of view it speed, facilitate, and improve the task-related functions. On the other hand, spending two third of our life within the workplace, meeting our psychological needs inn a group, and spending two third of our adult life in a work setting of various kinds, groups become a integral part of such work settings (Schein 1994:152). Thus, an enormous potential can be offered mixing up informal and formal functions, to comprehend it means to imagine how they can serve at the same both organisational and individual. Reed supported this thesis stating understand organisations means grasp the diverse political forces acting in it, nevertheless, decisions are not taken during a board of director, rather main actors discuss and reach agreement during a dinner on a golf course (2002). In other words, linking together individual’s needs and organisational functions to fulfil, by means of formal and informal organisation could be achieved, through effectiveness and the right balance with the social needs of employees, an organisational competitive advantage. The Socio Technical System (STS) Understand the dynamic process made up of individual’s needs interacting in organisational setting it is not as easy as at a first sight. After two decades in which the human relation (HR) approach allocate ‘attention to the employees, not work condition per se, that has the dominant impact on productivity (Peters & Waterman, cited in Moldaschl & Weber 1998:350), the sociotechnical group took another direction. Researches, associated with the work done by the Tavistock Institute in London, instead of concentrating on the enterprise as social system -where technology was not considered and workers were treated better whilst their job remained the same (Trist, in Moldaschl & Weber 1998), attempted to overcome both Tayloristic and HR approach of work design. Whereas the HR movement achieved the so-called ‘Hawthorne public relation effect’ -enforcing psychotechnics to deal with employees’ psychological ‘wealth’, STS underlined the importance of a real design of tasks (Emery 1978). The idea of STS implies that any productive organisation or part thereof is a combination of technology and social system in mutual interaction to each other. Each determines each other and the nature of work determines the type of organisation that develops among workers, whilst the sociopsychological characteristics of the worker determine the manner in which a given job will be performed (Schein 1994). This idea led to the development of an open system theory in which organisations imports and converts various things from its environment -such as people, money equipment, raw material, and so on, and exports products, services and waste materials which result from the conversion’s process (Schein 1994). Importing people the organisation have to deal with individual’s needs, values, norms, and expectations, as a consequence, to be effective the organisation have to take in account both the nature of job and those of people. Through the Norwegian â€Å"Industrial Democracy Programmes† sponsored by the government, the employer association, and unions, STS achieved a value-free research far from the political justification for self-governance and from the economic justification of self-regulation (Susman in Moldaschl & Weber 1998:350). It led their researchers to claim a third realization through the so called principle of industrial democracy -whilst for others concentrating their efforts on the micro level of participation, and neglecting representative forms of industrial democracy they realized just direct workplace democracy (Blackler 1982 in Moldaschl & Weber 1998). Another important concept is based on the joint optimisation through which it is possible developing design solutions that consider human criteria and efficiency criteria equally (Brown 2003). Thus, it â€Å"enables a best match in this way†¦such as Emery’s ‘nine-step model’ that aims to reduce â€Å"key variances† in, and between work systems, and to control them by â€Å"self-regulation† of the workers’ (Moldaschl & Weber 1998:360). This self-regulation, interdependence and self-governance, draw attention to decisions that ca be delegated to work groups that, in function of these, are defined as autonomous work group. In some industries has been discovered that higher levels of productivity and quality can be achieved giving clusters of tasks to a work group (Findlay et al, 2000; Barker 1999; Knights and McCabe 2000; Muller 1992; Sewell 1998); such ‘autonomous work groups are then made responsible for producing entire product such a radio, an engine’ (Schein 1994). The idea was to group several workers -organised in multifunctional structure with flexible job rotation, in a spatially and organisationally limited production unit, share a common task that is divided into interdependent sub task, and assume share responsibility over the long term. Among its criteria can be notice boundary maintenance (Moldaschl & Weber 1998:360). What sociotechnology group tried to achieve through the implement of autonomous work group is a way of simultaneously satisfying psychological and task needs (Buchanan 2000:29). In other words, a whole group is provided the opportunity to design and manage a total integrated task, thus permitting workers to fulfil their social and self actualising needs within the context of the work situation’ (Herbst 1962 in Schein 1994:195). Nevertheless being the role of management present to some extents, it is more correct to speak about semi autonomous work groups. Among the variety of semi-autonomous work group, it is useful to adopt the three forms identified by Brown (2003). The composite fully multi skilled -as in the Tavistock Institute Coal Mining studies where miners learnt and performed diverse task; the matrix form -as in Fiorelli’s idea of quality circle where a group of people, having different specialised functions, overlapped competences (1998); and the network where individuals are far but frequently in contact to each other through information technologies such as teleconferencing to exchange knowledge – from which the ongoing ‘knowledge management team’ (Bell, Blackler and Crump in Fulop & Linstead 1999:228). This tri-partition can be associated with changes in the second half of twentieth century in western society where ‘technological and organisational improvement led radical changes in economical sector’ (Ackroyd and Lawernson 1995, Piore & Sabel 1984, Zuboff 1998). Especially during the last three decades of the twenties century, after a climate of tension, a new international distension opened up new opportunities for businesses and ventures, new markets were found available to be explored and offered new competitive advantages to companies, (Hutton 2002). The re-design of the organisational structure bring in fact some effects within the socio-economical system where it is embedded. International markets got crowded; pressure and competition increased forcing companies to redesign their organisation. To face this turbulent environment Trist et al propose: ‘an alternative design based on the redundancies of functions: for individual they create role rather mere jobs; for the organisation they bring into being a variety-increasing system rather than the traditional control by variety reduction†¦(through) continuing development of appropriate new values concerned with improving the quality of working life by keeping the technological determinants of worker behaviour to a minimum in order to satisfy social and psychological needs by the involvement of all. Autonomous working groups, collaboration instead competitions, and reduction of hierarchical emphasis, are some of the requirements for operating effectively in modern turbulence (in Pugh & Hickson 1996:182 -emphasis added) As stated by Trist within this theoretical pattern, autonomous work group is an essential ingredient for the effective organising. Discussion and conclusion The role of management seems to be an essential component to the achievement of the best match within the system for both Blackler and Brown (1978), and Fox (1995), whilst strangely, STS approach does not seems to explicitly address neither the problem of management, nor those of managerial control. Differently, Knights & McCabe (2000) exploring what team working means for employees’ lives within an automobile manufacture company, affirm that employees as well as managers are capable of exercise power interpreting and reinterpreting management strategies. Stressing the accent on autonomy, managerial role need to be redefined to support and favourite tasks of group members. Accordingly, to meet autonomous work group needs a manager should be a good diagnostician, trying to be flexible enough to understand and to vary their own behaviour in relation to the needs of their subordinates (Schein 1994). Nevertheless, it is useful remember that individuals’ needs are not just meet through groups, they have another set of necessity that are fulfilled outside the group, alone, as well as with a friend. What I am addressing here is what Costea and Crump called the standardisation of individual -or better how to make an individual as unique as its mate (2003). In other words to be effective in self managing groups members have to maintain their equilibrium that permits them to keep and evolve its personality: members are not asked to follows rules, rather to make decisions. For this reason Often, the practical one does not confirm what in academic setting appear feasible from a conceptual level. Even for the best social scientist it is quite hard, if not impossible, individuate a priori the huge amount of forces arising from the combination of interests and pressure groups in which his theory will become part. In practical conditions, sociotechnical projects sometimes failed because they subordinate human criteria to the dictates of efficiency or because they become victim of a political conflicts (Blackler, 1982; Kelly, 1978; Sydow, 1985; Pasmore, 1995 in Moldaschl & Weber 1998), making it often impossible to translate joint optimisation of human goals and efficiency into reality. ‘Although mainly consisting of psychologist of work and organisation, the â€Å"classical† Tavistock representatives of the STS approach does not regard its primary goal to be the far reaching consideration of human criteria in the design process of a work system. Rather they st rive for an optimal compromise between technical, economic, and human work design objectives’ (Moldaschl & Weber 1998:362). Changing our analysis from a classical to more contemporaneous perspective, a diverse slant come from the observation that self managing groups are still effective, but they loose their grip on organisation when have to deal with the no-routine office work of management and professional -being these set of practices developed for linear work systems (Fox 1995). Diverse from Pugh and Hickson (1986), Fox notes that not always the use of autonomous work group seems to be appropriate, in fact ‘the creation of recticular organisation (characterised by a fluid distribution of information and authority that changes are required) may be appropriate†¦in some non linear work systems (1995:103). STS’ concepts have contributed to improve design and redesign of many work systems, however most of the successful experiences occurred in well-defined linear systems-characterised by a sequential process of input-output, rather in unclear defined non-linear system -where the absence of the in-out property makes it difficult to separate different conversion flows into well-bounded entities (Pava, 1986). Nevertheless, a major revolution is not required to broaden the applicability of STS principles: Modifying the practices employed in STS design to include non-linear work systems is consistent with the essential precepts of STS design: open system analysis, a best match of social and technical subsystems, redundant functions over redundant parts, systemic interrelationships between design factors, self-design, and critical specification (Pava 211). In this capacity to adapt itself in both changing organisational requirements and environment, I think should be recognised the bigger strength of STS. Becoming this adaptability without distort any principle, the approach seems to be relevant especially nowadays, seeking organisations new means of empowerment to boost the productivity in increasingly turbulent environment. A final consideration is due to the work Manz who argue, the future of self-managing groups seems be oriented to lead workers to lead themselves (1992). During this movement toward a self-leading team type of work design, the latter identify some contingency factors relevant to this transition such as: nature of workers; work context; new manufacturing techniques; environment; and organisational system. However, this model seems more likely applicable in such culture where both high trust to workers and decentralisation of power is given -i.e. UK as opposite to Japan and Germany. In fact, ‘Movement toward self-leading team work likely to require significant involvement of the work force in determining the direction of the organisation as well as carrying out that direction, and the opportunity for the work teams to influence that direction, especially as it relates to their specific work performance’ (Manz 1992). Within this framework, it possible imagine shift from traditional & participative leadership to a self management role of leader, in doing it, the new role will be to lead members’ group to lead themselves (Manz & Sims 1987). Being both the power shifting from managers to team members, and the latter able to distinguish true managerial aptitudes from artificial (Knights & McCabe 2000), a certain amount of resistance from the former could be assumed. It leads to pay attention on the way in which managers implement these set of practices. In conclusion, due to its adaptability to technological innovations, and its flexibility in linear and non linear systems autonomous work group could seems even more actual today than during the second half of the second century. Its democratic principles and the democratic way in which tasks are thought and accomplished, seems to make this system the most appropriate within those political environment in which principles of democracy are used. This thesis seems reinforced from the growth of lean systems and consequently from practices as Just in Time, Business Process Re-engineering, or Total Quality Management in those organisational setting where work design diverse from human centred. On the base of both the literature proposed, and the assumption resting on this paper, an important feature seems emerge. For those organisations pursuing human relations and democratic policies, autonomous work group permits both individual and organisations to pursue their own interests. Not just offering the opportunity to decrease alienation filling their social needs to the former, and to reduce practice such as of absenteeism, sabotage, and achieve that commitment and loyalty, to the latter. Rather it seems the best compromise between capitalism and working class since the first industrial revolution to nowadays. An effective tool capable to improves and re-defines the boundaries of the psychological contract and consecutively boosts productivity and reduces costs. To create effective self-managing groups become central the role of top management in planning and develop a long-term program made of continuous investment in work design research, and in staff and management programs (Pearson 1992). It will allow a deep understanding about the dynamics of members’ needs, a constant design, a re-negation of the task requirements, and to avoid both mismanagement, and the establishment of repetitive alienating tasks. Finally, to figure out this sophisticated topic, a broader research should analyse the interrelation and influences of related issue such as: identifications; role of control; ideology of team, politico-economic and socio-cultural peculiarity of the society; in which the organisation will decide to implement self management group working. Within this system, autonomous work group seems to be not a problem to be solved, rather a solution to deal today with the confluence of tensions resulting from yesterday’s decisions.

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