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Author : Ake Bjorck
Publisher : SIAM
Page : 421 pages
File Size : 54,6 Mb
Release : 1996-12-01
Category : Mathematics
ISBN : 9780898713602
The method of least squares: the principal tool for reducing the influence of errors when fitting models to given observations.
Author : Charles L. Lawson,Richard J. Hanson
Publisher : SIAM
Page : 348 pages
File Size : 51,6 Mb
Release : 1995-12-01
Category : Mathematics
ISBN : 9780898713565
This Classic edition includes a new appendix which summarizes the major developments since the book was originally published in 1974. The additions are organized in short sections associated with each chapter. An additional 230 references have been added, bringing the bibliography to over 400 entries. Appendix C has been edited to reflect changes in the associated software package and software distribution method.
Author : Sabine Van Huffel,Joos Vandewalle
Publisher : SIAM
Page : 302 pages
File Size : 46,5 Mb
Release : 1991-01-01
Category : Mathematics
ISBN : 9780898712759
This is the first book devoted entirely to total least squares. The authors give a unified presentation of the TLS problem. A description of its basic principles are given, the various algebraic, statistical and sensitivity properties of the problem are discussed, and generalizations are presented. Applications are surveyed to facilitate uses in an even wider range of applications. Whenever possible, comparison is made with the well-known least squares methods. A basic knowledge of numerical linear algebra, matrix computations, and some notion of elementary statistics is required of the reader; however, some background material is included to make the book reasonably self-contained.
Author : Åke Björck
Publisher : Unknown
Page : 0 pages
File Size : 52,6 Mb
Release : 2024-07
Category : Mathematics
ISBN : 1611977940
Author : Pavel B. Bochev,Max D. Gunzburger
Publisher : Springer Science & Business Media
Page : 669 pages
File Size : 52,8 Mb
Release : 2009-04-28
Category : Mathematics
ISBN : 9780387689227
Since their emergence, finite element methods have taken a place as one of the most versatile and powerful methodologies for the approximate numerical solution of Partial Differential Equations. These methods are used in incompressible fluid flow, heat, transfer, and other problems. This book provides researchers and practitioners with a concise guide to the theory and practice of least-square finite element methods, their strengths and weaknesses, established successes, and open problems.
Author : James W. Demmel
Publisher : SIAM
Page : 426 pages
File Size : 43,8 Mb
Release : 1997-08-01
Category : Mathematics
ISBN : 9780898713893
This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.
Author : Åke Björck
Publisher : Springer
Page : 800 pages
File Size : 51,6 Mb
Release : 2014-10-07
Category : Mathematics
ISBN : 9783319050898
Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work.
Author : Ilse C. F. Ipsen
Publisher : SIAM
Page : 135 pages
File Size : 42,8 Mb
Release : 2009-07-23
Category : Mathematics
ISBN : 9780898716764
Matrix analysis presented in the context of numerical computation at a basic level.
Author : Bo-nan Jiang
Publisher : Springer Science & Business Media
Page : 425 pages
File Size : 45,8 Mb
Release : 2013-03-14
Category : Science
ISBN : 9783662037409
This is the first monograph on the subject, providing a comprehensive introduction to the LSFEM method for numerical solution of PDEs. LSFEM is simple, efficient and robust, and can solve a wide range of problems in fluid dynamics and electromagnetics.
Author : Ilse C. F. Ipsen
Publisher : SIAM
Page : 136 pages
File Size : 44,5 Mb
Release : 2009-01-01
Category : Mathematics
ISBN : 9780898717686
The purpose of this book is to promote understanding of two phenomena: sensitivity of linear systems and least squares problems, and numerical stability of algorithms. Sensitivity and stability are analyzed as mathematical properties, without reference to finite precision arithmetic. The material is presented at a basic level, emphasizing ideas and intuition, but in a mathematically rigorous fashion. The derivations are simple and elegant, and the results are easy to understand and interpret. The book is self-contained. It was written for students in all areas of mathematics, engineering, and the computational sciences, but can easily be used for self-study. This text differs from other numerical linear algebra texts by offering the following: a systematic development of numerical conditioning; a simplified concept of numerical stability in exact arithmetic; simple derivations; a high-level view of algorithms; and results for complex matrices.
Author : Justin Solomon
Publisher : CRC Press
Page : 400 pages
File Size : 41,7 Mb
Release : 2015-06-24
Category : Computers
ISBN : 9781482251890
Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig
Author : John C. Nash
Publisher : CRC Press
Page : 298 pages
File Size : 40,5 Mb
Release : 1990-01-01
Category : Mathematics
ISBN : 085274319X
This second edition of Compact Numerical Methods for Computers presents reliable yet compact algorithms for computational problems. As in the previous edition, the author considers specific mathematical problems of wide applicability, develops approaches to a solution and the consequent algorithm, and provides the program steps. He emphasizes useful applicable methods from various scientific research fields, ranging from mathematical physics to commodity production modeling. While the ubiquitous personal computer is the particular focus, the methods have been implemented on computers as small as a programmable pocket calculator and as large as a highly parallel supercomputer. New to the Second Edition Presents program steps as Turbo Pascal code Includes more algorithmic examples Contains an extended bibliography The accompanying software (available by coupon at no charge) includes not only the algorithm source codes, but also driver programs, example data, and several utility codes to help in the software engineering of end-user programs. The codes are designed for rapid implementation and reliable use in a wide variety of computing environments. Scientists, statisticians, engineers, and economists who prepare/modify programs for use in their work will find this resource invaluable. Moreover, since little previous training in numerical analysis is required, the book can also be used as a supplementary text for courses on numerical methods and mathematical software.
Author : Guy Chavent
Publisher : Springer Science & Business Media
Page : 366 pages
File Size : 44,9 Mb
Release : 2010-03-14
Category : Mathematics
ISBN : 9789048127856
The domain of inverse problems has experienced a rapid expansion, driven by the increase in computing power and the progress in numerical modeling. When I started working on this domain years ago, I became somehow fr- tratedtoseethatmyfriendsworkingonmodelingwhereproducingexistence, uniqueness, and stability results for the solution of their equations, but that I was most of the time limited, because of the nonlinearity of the problem, to provethatmyleastsquaresobjectivefunctionwasdi?erentiable....Butwith my experience growing, I became convinced that, after the inverse problem has been properly trimmed, the ?nal least squares problem, the one solved on the computer, should be Quadratically (Q)-wellposed,thatis,both we- posed and optimizable: optimizability ensures that a global minimizer of the least squares function can actually be found using e?cient local optimization algorithms, and wellposedness that this minimizer is stable with respect to perturbation of the data. But the vast majority of inverse problems are nonlinear, and the clas- cal mathematical tools available for their analysis fail to bring answers to these crucial questions: for example, compactness will ensure existence, but provides no uniqueness results, and brings no information on the presence or absenceofparasiticlocalminimaorstationarypoints....
Author : J. E. Dennis, Jr.,Robert B. Schnabel
Publisher : SIAM
Page : 394 pages
File Size : 55,8 Mb
Release : 1996-12-01
Category : Mathematics
ISBN : 1611971209
This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or "quasi-Newton" methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems. The level of presentation is consistent throughout, with a good mix of examples and theory, making it a valuable text at both the graduate and undergraduate level. It has been praised as excellent for courses with approximately the same name as the book title and would also be useful as a supplemental text for a nonlinear programming or a numerical analysis course. Many exercises are provided to illustrate and develop the ideas in the text. A large appendix provides a mechanism for class projects and a reference for readers who want the details of the algorithms. Practitioners may use this book for self-study and reference. For complete understanding, readers should have a background in calculus and linear algebra. The book does contain background material in multivariable calculus and numerical linear algebra.
Author : Endre Süli,David F. Mayers
Publisher : Cambridge University Press
Page : 440 pages
File Size : 55,8 Mb
Release : 2003-08-28
Category : Mathematics
ISBN : 0521007941
An introduction to numerical analysis combining rigour with practical applications, and providing numerous exercises plus solutions.