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Author : Avram Sidi
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (475 download)
Download or read book Extrapolation vs Projection Methods for Linear Systems of Equations written by Avram Sidi and published by . This book was released on 1987 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : C. Brezinski
Publisher : North Holland
ISBN 13 :
Total Pages : 416 pages
Book Rating : 4.F/5 ( download)
Download or read book Projection Methods for Systems of Equations written by C. Brezinski and published by North Holland. This book was released on 1997-12-09 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers the problem of solving a nonsingular system of linear equations by an iterative method. The work is primarily intended for researchers in the field, but it can also be useful for engineers and practitioners. Coverage includes topics such as projection methods, solving linear systems by extrapolation, biorthogonality, Lanczos-type methodologies, Richardson's projection, quasi- Newton methods, and some fixed point methods. Appends Schur's complement and Sylvester's and Schweins' identities. Includes an extensive bibliography. Annotation copyrighted by Book News, Inc., Portland, OR
Author : Avram Sidi
Publisher : SIAM
ISBN 13 : 161197495X
Total Pages : 421 pages
Book Rating : 4.6/5 (119 download)
Download or read book Vector Extrapolation Methods with Applications written by Avram Sidi and published by SIAM. This book was released on 2017-09-26 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: An important problem that arises in different disciplines of science and engineering is that of computing limits of sequences of vectors of very large dimension. Such sequences arise, for example, in the numerical solution of systems of linear and nonlinear equations by fixed-point iterative methods, and their limits are simply the required solutions to these systems. The convergence of these sequences, which is very slow in many cases, can be accelerated successfully by using suitable vector extrapolation methods. Vector Extrapolation Methods with Applications?is the first book fully dedicated to the subject of vector extrapolation methods. It is a self-contained, up-to-date, and state-of-the-art reference on the theory and practice of the most useful methods. It covers all aspects of the subject, including development of the methods, their convergence study, numerically stable algorithms for their implementation, and their various applications. It also provides complete proofs in most places. As an interesting application, the author shows how these methods give rise to rational approximation procedures for vector-valued functions in the complex plane, a subject of importance in model reduction problems among others. This book is intended for numerical analysts, applied mathematicians, and computational scientists and engineers in fields such as computational fluid dynamics, structures, and mechanical and electrical engineering, to name a few. Since it provides complete proofs in most places, it can also serve as a textbook in courses on acceleration of convergence of iterative vector processes, for example.
Author : C. Brezinski
Publisher : Elsevier
ISBN 13 : 0080506224
Total Pages : 475 pages
Book Rating : 4.0/5 (85 download)
Download or read book Extrapolation Methods written by C. Brezinski and published by Elsevier. This book was released on 2013-10-24 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a self-contained, exhaustive exposition of the extrapolation methods theory, and of the various algorithms and procedures for accelerating the convergence of scalar and vector sequences. Many subroutines (written in FORTRAN 77) with instructions for their use are provided on a floppy disk in order to demonstrate to those working with sequences the advantages of the use of extrapolation methods. Many numerical examples showing the effectiveness of the procedures and a consequent chapter on applications are also provided – including some never before published results and applications. Although intended for researchers in the field, and for those using extrapolation methods for solving particular problems, this volume also provides a valuable resource for graduate courses on the subject.
Author : Claude Brezinski
Publisher : Springer Nature
ISBN 13 : 3030584186
Total Pages : 410 pages
Book Rating : 4.0/5 (35 download)
Download or read book Extrapolation and Rational Approximation written by Claude Brezinski and published by Springer Nature. This book was released on 2020-11-30 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book paints a fresco of the field of extrapolation and rational approximation over the last several centuries to the present through the works of their primary contributors. It can serve as an introduction to the topics covered, including extrapolation methods, Padé approximation, orthogonal polynomials, continued fractions, Lanczos-type methods etc.; it also provides in depth discussion of the many links between these subjects. A highlight of this book is the presentation of the human side of the fields discussed via personal testimonies from contemporary researchers, their anecdotes, and their exclusive remembrances of some of the “actors.” This book shows how research in this domain started and evolved. Biographies of other scholars encountered have also been included. An important branch of mathematics is described in its historical context, opening the way to new developments. After a mathematical introduction, the book contains a precise description of the mathematical landscape of these fields spanning from the 19th century to the first part of the 20th. After an analysis of the works produced after that period (in particular those of Richardson, Aitken, Shanks, Wynn, and others), the most recent developments and applications are reviewed.
Author : Yousef Saad
Publisher : SIAM
ISBN 13 : 9780898718003
Total Pages : 546 pages
Book Rating : 4.7/5 (18 download)
Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-01-01 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the first edition of this book was published in 1996, tremendous progress has been made in the scientific and engineering disciplines regarding the use of iterative methods for linear systems. The size and complexity of the new generation of linear and nonlinear systems arising in typical applications has grown. Solving the three-dimensional models of these problems using direct solvers is no longer effective. At the same time, parallel computing has penetrated these application areas as it became less expensive and standardized. Iterative methods are easier than direct solvers to implement on parallel computers but require approaches and solution algorithms that are different from classical methods. Iterative Methods for Sparse Linear Systems, Second Edition gives an in-depth, up-to-date view of practical algorithms for solving large-scale linear systems of equations. These equations can number in the millions and are sparse in the sense that each involves only a small number of unknowns. The methods described are iterative, i.e., they provide sequences of approximations that will converge to the solution.
Author : Yousef Saad
Publisher : SIAM
ISBN 13 : 0898715342
Total Pages : 537 pages
Book Rating : 4.8/5 (987 download)
Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.
Author : Janusz S. Kowalik
Publisher : Springer Science & Business Media
ISBN 13 : 3642757715
Total Pages : 416 pages
Book Rating : 4.6/5 (427 download)
Download or read book Supercomputing written by Janusz S. Kowalik and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Supercomputing is an important science and technology that enables the scientist or the engineer to simulate numerically very complex physical phenomena related to large-scale scientific, industrial and military applications. It has made considerable progress since the first NATO Workshop on High-Speed Computation in 1983 (Vol. 7 of the same series). This book is a collection of papers presented at the NATO Advanced Research Workshop held in Trondheim, Norway, in June 1989. It presents key research issues related to: - hardware systems, architecture and performance; - compilers and programming tools; - user environments and visualization; - algorithms and applications. Contributions include critical evaluations of the state-of-the-art and many original research results.
Author : C. Brezinski
Publisher : Elsevier
ISBN 13 : 0444598588
Total Pages : 512 pages
Book Rating : 4.4/5 (445 download)
Download or read book Numerical Analysis: Historical Developments in the 20th Century written by C. Brezinski and published by Elsevier. This book was released on 2012-12-02 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical analysis has witnessed many significant developments in the 20th century. This book brings together 16 papers dealing with historical developments, survey papers and papers on recent trends in selected areas of numerical analysis, such as: approximation and interpolation, solution of linear systems and eigenvalue problems, iterative methods, quadrature rules, solution of ordinary-, partial- and integral equations. The papers are reprinted from the 7-volume project of the Journal of Computational and Applied Mathematics on '/homepage/sac/cam/na2000/index.htmlNumerical Analysis 2000'. An introductory survey paper deals with the history of the first courses on numerical analysis in several countries and with the landmarks in the development of important algorithms and concepts in the field.
Author : Claude Brezinski
Publisher : CRC Press
ISBN 13 : 1000104737
Total Pages : 181 pages
Book Rating : 4.0/5 (1 download)
Download or read book Biorthogonality and its Applications to Numerical Analysis written by Claude Brezinski and published by CRC Press. This book was released on 2020-08-11 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the use of the concept of biorthogonality and discusses the various recurrence relations for the generalizations of the method of moments, the method of Lanczos, and the biconjugate gradient method. It is helpful for researchers in numerical analysis and approximation theory.
Author : Roger L. Wainwright
Publisher :
ISBN 13 :
Total Pages : 135 pages
Book Rating : 4.:/5 (184 download)
Download or read book Algorithms for Projection Methods for Solving Linear Systems of Equations written by Roger L. Wainwright and published by . This book was released on 1974 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. David Brown
Publisher : SIAM
ISBN 13 : 9780898713398
Total Pages : 722 pages
Book Rating : 4.7/5 (133 download)
Download or read book Proceedings of the Cornelius Lanczos International Centenary Conference written by J. David Brown and published by SIAM. This book was released on 1994-01-01 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Zahari Zlatev
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110533006
Total Pages : 310 pages
Book Rating : 4.1/5 (15 download)
Download or read book Richardson Extrapolation written by Zahari Zlatev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-11-07 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientists and engineers are mainly using Richardson extrapolation as a computational tool for increasing the accuracy of various numerical algorithms for the treatment of systems of ordinary and partial differential equations and for improving the computational efficiency of the solution process by the automatic variation of the time-stepsizes. A third issue, the stability of the computations, is very often the most important one and, therefore, it is the major topic studied in all chapters of this book. Clear explanations and many examples make this text an easy-to-follow handbook for applied mathematicians, physicists and engineers working with scientific models based on differential equations. Contents The basic properties of Richardson extrapolation Richardson extrapolation for explicit Runge-Kutta methods Linear multistep and predictor-corrector methods Richardson extrapolation for some implicit methods Richardson extrapolation for splitting techniques Richardson extrapolation for advection problems Richardson extrapolation for some other problems General conclusions
Author : Curtis J. Anderson
Publisher :
ISBN 13 :
Total Pages : 54 pages
Book Rating : 4.:/5 (127 download)
Download or read book Estimating the Optimal Extrapolation Parameter for Extrapolated Iterative Methods when Solving Sequences of Linear Systems written by Curtis J. Anderson and published by . This book was released on 2013 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extrapolated iterative methods for solving systems of linear equations require the selection of an extrapolation parameter which greatly influences the rate of convergence. Some extrapolated iterative methods provide analysis on the optimal extrapolation parameter to use, however, such analysis only exists for specific problems and a general method for parameter selection does not exist. Additionally, the calculation of the optimal extrapolation parameter can often be too computationally expensive to be of practical use. This thesis presents an algorithm that will adaptively modify the extrapolation parameter when solving a sequence of linear systems in order to estimate the optimal extrapolation parameter. The result is an algorithm that works for any general problem and requires very little computational overhead. Statistics on the quality of the algorithm's estimation are presented and a case study is given to show practical results.
Author : C. B. Liem
Publisher : World Scientific
ISBN 13 : 9789810222178
Total Pages : 344 pages
Book Rating : 4.2/5 (221 download)
Download or read book The Splitting Extrapolation Method written by C. B. Liem and published by World Scientific. This book was released on 1995 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The splitting extrapolation method is a newly developed technique for solving multidimensional mathematical problems. It overcomes the difficulties arising from Richardson's extrapolation when applied to these problems and obtains higher accuracy solutions with lower cost and a high degree of parallelism. The method is particularly suitable for solving large scale scientific and engineering problems.This book presents applications of the method to multidimensional integration, integral equations and partial differential equations. It also gives an introduction to combination methods which are relevant to splitting extrapolation. The book is intended for those who may exploit these methods and it requires only a basic knowledge of numerical analysis.
Author : Avram Sidi
Publisher :
ISBN 13 :
Total Pages : 62 pages
Book Rating : 4.:/5 (317 download)
Download or read book Upper Bounds for Convergence Rates of Vector Extrapolation Methods on Linear Systems with Initial Iterations written by Avram Sidi and published by . This book was released on 1991 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : D. Butnariu
Publisher : Elsevier
ISBN 13 : 0080508766
Total Pages : 515 pages
Book Rating : 4.0/5 (85 download)
Download or read book Inherently Parallel Algorithms in Feasibility and Optimization and their Applications written by D. Butnariu and published by Elsevier. This book was released on 2001-06-18 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Haifa 2000 Workshop on "Inherently Parallel Algorithms for Feasibility and Optimization and their Applications" brought together top scientists in this area. The objective of the Workshop was to discuss, analyze and compare the latest developments in this fast growing field of applied mathematics and to identify topics of research which are of special interest for industrial applications and for further theoretical study.Inherently parallel algorithms, that is, computational methods which are, by their mathematical nature, parallel, have been studied in various contexts for more than fifty years. However, it was only during the last decade that they have mostly proved their practical usefulness because new generations of computers made their implementation possible in order to solve complex feasibility and optimization problems involving huge amounts of data via parallel processing. These led to an accumulation of computational experience and theoretical information and opened new and challenging questions concerning the behavior of inherently parallel algorithms for feasibility and optimization, their convergence in new environments and in circumstances in which they were not considered before their stability and reliability. Several research groups all over the world focused on these questions and it was the general feeling among scientists involved in this effort that the time has come to survey the latest progress and convey a perspective for further development and concerted scientific investigations. Thus, the editors of this volume, with the support of the Israeli Academy for Sciences and Humanities, took the initiative of organizing a Workshop intended to bring together the leading scientists in the field. The current volume is the Proceedings of the Workshop representing the discussions, debates and communications that took place. Having all that information collected in a single book will provide mathematicians and engineers interested in the theoretical and practical aspects of the inherently parallel algorithms for feasibility and optimization with a tool for determining when, where and which algorithms in this class are fit for solving specific problems, how reliable they are, how they behave and how efficient they were in previous applications. Such a tool will allow software creators to choose ways of better implementing these methods by learning from existing experience.
