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Author: Eugene L. Allgower
Publisher: SIAM
ISBN: 9780898719154
Category : Mathematics
Languages : en
Pages : 413
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Book Description
Numerical continuation methods have provided important contributions toward the numerical solution of nonlinear systems of equations for many years. The methods may be used not only to compute solutions, which might otherwise be hard to obtain, but also to gain insight into qualitative properties of the solutions. Introduction to Numerical Continuation Methods, originally published in 1979, was the first book to provide easy access to the numerical aspects of predictor corrector continuation and piecewise linear continuation methods. Not only do these seemingly distinct methods share many common features and general principles, they can be numerically implemented in similar ways. The book also features the piecewise linear approximation of implicitly defined surfaces, the algorithms of which are frequently used in computer graphics, mesh generation, and the evaluation of surface integrals. To help potential users of numerical continuation methods create programs adapted to their particular needs, this book presents pseudo-codes and Fortran codes as illustrations. Since it first appeared, many specialized packages for treating such varied problems as bifurcation, polynomial systems, eigenvalues, economic equilibria, optimization, and the approximation of manifolds have been written. The original extensive bibliography has been updated in the SIAM Classics edition to include more recent references and several URLs so users can look for codes to suit their needs. Audience: this book continues to be useful for researchers and graduate students in mathematics, sciences, engineering, economics, and business. A background in elementary analysis and linear algebra are adequate prerequisites for reading this book; some knowledge from a first course in numerical analysis may also be helpful.
Author: Eugene L. Allgower
Publisher: SIAM
ISBN: 9780898719154
Category : Mathematics
Languages : en
Pages : 413
Get Book Here
Book Description
Numerical continuation methods have provided important contributions toward the numerical solution of nonlinear systems of equations for many years. The methods may be used not only to compute solutions, which might otherwise be hard to obtain, but also to gain insight into qualitative properties of the solutions. Introduction to Numerical Continuation Methods, originally published in 1979, was the first book to provide easy access to the numerical aspects of predictor corrector continuation and piecewise linear continuation methods. Not only do these seemingly distinct methods share many common features and general principles, they can be numerically implemented in similar ways. The book also features the piecewise linear approximation of implicitly defined surfaces, the algorithms of which are frequently used in computer graphics, mesh generation, and the evaluation of surface integrals. To help potential users of numerical continuation methods create programs adapted to their particular needs, this book presents pseudo-codes and Fortran codes as illustrations. Since it first appeared, many specialized packages for treating such varied problems as bifurcation, polynomial systems, eigenvalues, economic equilibria, optimization, and the approximation of manifolds have been written. The original extensive bibliography has been updated in the SIAM Classics edition to include more recent references and several URLs so users can look for codes to suit their needs. Audience: this book continues to be useful for researchers and graduate students in mathematics, sciences, engineering, economics, and business. A background in elementary analysis and linear algebra are adequate prerequisites for reading this book; some knowledge from a first course in numerical analysis may also be helpful.
Author: Stephen M. Robinson
Publisher: Academic Press
ISBN: 1483266028
Category : Mathematics
Languages : en
Pages : 424
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Book Description
Analysis and Computation of Fixed Points contains the proceedings of a Symposium on Analysis and Computation of Fixed Points, held at the University of Wisconsin-Madison on May 7-8, 1979. The papers focus on the analysis and computation of fixed points and cover topics ranging from paths generated by fixed point algorithms to strongly stable stationary solutions in nonlinear programs. A simple reliable numerical algorithm for following homotopy paths is also presented. Comprised of nine chapters, this book begins by describing the techniques of numerical linear algebra that possess attractive stability properties and exploit sparsity, and their application to the linear systems that arise in algorithms that solve equations by constructing piecewise-linear homotopies. The reader is then introduced to two triangulations for homotopy fixed point algorithms with an arbitrary grid refinement, followed by a discussion on some generic properties of paths generated by fixed point algorithms. Subsequent chapters deal with topological perturbations in the numerical study of nonlinear eigenvalue and bifurcation problems; general equilibrium analysis of taxation policy; and solving urban general equilibrium models by fixed point methods. The book concludes with an evaluation of economic equilibrium under deformation of the economy. This monograph should be of interest to students and specialists in the field of mathematics.
Author: U. Witt
Publisher: Springer Science & Business Media
ISBN: 3642483259
Category : Business & Economics
Languages : en
Pages : 275
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Book Description
Author: P. M. C. de Boer
Publisher: Springer Science & Business Media
ISBN: 3642464602
Category : Business & Economics
Languages : en
Pages : 153
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Book Description
1.1. Pre Ziminary remarks Input-output analysis is one of the most extensively used tools of economic science. It has been introduced by Leontief (1941) who assumed that inputs into a production process of a particular sector of economic activity is a constant fraction of the output of that process in physicaZ terms. National account statisticians, however, record the inputs and outputs of sectors of economic activity in money flows. If those flows were voZumes (evalu ated at constant prices, pertaining to a certain base year) they could represent the physical amounts Leontief dealt with. Then, the Leontief assumption turns into constancy of ratios of volumes of inputs to volumes of output. For an over view of (traditional) input-output analysis we refer to section 4.1.1. In practice, however, input-output tables in volumes are seldom available; since as a rule they are expressed in monetary vaZues (i.e. evaluated at current prices). In that case one generally assumes that the ratios between inputs (in value terms) and outputs (in value terms) are constant. In appendix B to chapter 4 we prove that the two variants described above can be couched in terms of the (neo-classical) theory of costs subject to a production function.
Author: H. Siebert
Publisher: Springer Science & Business Media
ISBN: 364246484X
Category : Business & Economics
Languages : en
Pages : 174
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Book Description
the economics of exhaustible " assets presents a whole forest of intriguing problems." 1 Harald Hotelling ) The two energy price shocks in 1973/74 and 1979/80 have arosed interest in the new area of resource economics. The affluent societies of Europe, North America and Japan were confronted with the new scarcity paradigm of the "space ship earth" with only a limited supply of natural resources aboard whereas population is growing and the environment can not accomodate the increasing volume of pollutants. The problem of natural resource scarcity gives rise to the question how resource-dependent economies like European coun tries and Japan are affected by an increase in resource prices and how they can adjust to rising energy prices. The new para digm also has focused new interest on the problem of the re source-extracting firm and of the resource-exporting country. The Hotelling revival of resource economics has given new im portance to the behavior and to the policy issues of resource exporting countries.
Author: R. Ramanathan
Publisher: Springer Science & Business Media
ISBN: 3642455417
Category : Business & Economics
Languages : en
Pages : 358
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Book Description
This book is an outgrowth of years of teaching and doing re search at the University of California, San Diego (UCSD), in the area of economic growth. Although there have been several books on this topic published in the last eight years, I have been dis satisfied with them for several reasons. First, books such as those by Wan, Burmeister and Dobell are uneven in their technical difficulty and, while they are excellent, are apparently difficult for first year graduate students and advanced undergraduates. Solow's expository book, on the other hand, is at the other ex treme. Furthermore, many of the books seem to be aimed at the authors' peers rather than the students. My primary objective in writing this book is to bridge this gap and to pitch, very appro priately I hope, at the level of a typical student enrolled in a beginning course in growth theory. Secondly, almost all the growth models in the literature can be recast in a single analyti cal framework. Although the various authors have not written so as to conform to any particular pattern, it -is the function of a textbook writer to identify such a pattern, if it exists, and pre sent the theory in that framework. Many authors make implicit as sumptions about their models which are either never specified or sometimes specified in footnotes.
Author: M.H. Karwan
Publisher: Springer Science & Business Media
ISBN: 3642455352
Category : Business & Economics
Languages : en
Pages : 298
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Book Description
During the Spring of 1979 one of us (Zionts) was invited to visit Erasmus University in Rotterdam, The Netherlands. It was there that Zionts met another of us (Telgen) who was then in the process of completing a dissertation on redundancy in linear programming. At that time, Telgen proposed an extended visit to Buffalo, during which time he and Zionts would do an extensive study on redundancy. Redundancy, hardly an exciting or new topic, does have numerous applications. Telgen and Zionts planned the project for the Summer of 1980, and enlisted the support of all the contributors as well as the other two members of our team (Karwan and Lotfi). Lotfi was then a Ph. D. student in Industrial Engineering searching for a thesis topic. Redundancy became his topic. Karwan and Zionts served as his thesis co-chairmen, with Telgen serving as an outside reader of the thesis. We initially had hoped to complete the study during Telgen's stay in Buffalo, but that was far too optimistic. Lotfi completed his dissertation during the late Spring-early Summer of 1981. As the project took shape, we decided that we had more than enough for an article, or even several articles. Accordingly, not wanting to produce redundant papers, we decided to produce this volume --- a state-of-the-art review of methods for handling redundancy and comprehensive tests of the various methods, together with extensions and further developments of the most promising methods.
Author: J. V. Skolka
Publisher: Springer Science & Business Media
ISBN: 3642464629
Category : Business & Economics
Languages : en
Pages : 317
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Book Description
Those familiar with input-output analysis know well that compilation of input-output tables is a difficult statistical work. The very first input-output tables (e.g. such as those for the United States economy in 1919 and 1929 or for the Federal Republic of Germany in the fifties) were the results of applied economic research. But soon after, official statistical bodies, who understood that input-output tables consistent with national accounts can very much improve the quality of economic statistics, started systematic work in this field. It was also obvious that international exchange of experience can be useful. The two main internatio nal fora in which discussion of input-output compilation took place were the international input-out put conferences and United Nations bodies. Already at the First International Conference on Input-Output Techniques (Driebergen 1950) several authors analysed the relations between input-output tables and national accounts. The topic was also on the programme of the Second Conference (Varenna 1954). At the Third Conference (Geneva 1961) standardization of input-output statistics was a topic of a panel discussion of eight experts. The relevant papers, which are still of interest, can be found in published conference proceedings.
Author: R.v. Randow
Publisher: Springer Science & Business Media
ISBN: 3642464491
Category : Business & Economics
Languages : en
Pages : 349
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Book Description
Author: Eugene L. Allgower
Publisher: Springer Science & Business Media
ISBN: 3642612571
Category : Mathematics
Languages : en
Pages : 402
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Book Description
Over the past fifteen years two new techniques have yielded extremely important contributions toward the numerical solution of nonlinear systems of equations. This book provides an introduction to and an up-to-date survey of numerical continuation methods (tracing of implicitly defined curves) of both predictor-corrector and piecewise-linear types. It presents and analyzes implementations aimed at applications to the computation of zero points, fixed points, nonlinear eigenvalue problems, bifurcation and turning points, and economic equilibria. Many algorithms are presented in a pseudo code format. An appendix supplies five sample FORTRAN programs with numerical examples, which readers can adapt to fit their purposes, and a description of the program package SCOUT for analyzing nonlinear problems via piecewise-linear methods. An extensive up-to-date bibliography spanning 46 pages is included. The material in this book has been presented to students of mathematics, engineering and sciences with great success, and will also serve as a valuable tool for researchers in the field.
