Guaranteed Accuracy In Numerical Linear Algebra
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Guaranteed Accuracy In Numerical Linear Algebra
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Author : S.K. Godunov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Guaranteed Accuracy In Numerical Linear Algebra written by S.K. Godunov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
There exists a vast literature on numerical methods of linear algebra. In our bibliography list, which is by far not complete, we included some monographs on the subject [46], [15], [32], [39], [11], [21]. The present book is devoted to the theory of algorithms for a single problem of linear algebra, namely, for the problem of solving systems of linear equations with non-full-rank matrix of coefficients. The solution of this problem splits into many steps, the detailed discussion of which are interest ing problems on their own (bidiagonalization of matrices, computation of singular values and eigenvalues, procedures of deflation of singular values, etc. ). Moreover, the theory of algorithms for solutions of the symmetric eigenvalues problem is closely related to the theory of solv ing linear systems (Householder's algorithms of bidiagonalization and tridiagonalization, eigenvalues and singular values, etc. ). It should be stressed that in this book we discuss algorithms which to computer programs having the virtue that the accuracy of com lead putations is guaranteed. As far as the final program product is con cerned, this means that the user always finds an unambiguous solution of his problem. This solution might be of two kinds: 1. Solution of the problem with an estimate of errors, where abso lutely all errors of input data and machine round-offs are taken into account. 2.
Guaranteed Accuracy In Numerical Linear Algebra
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Author : S.K. Godunov
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-06-30
Guaranteed Accuracy In Numerical Linear Algebra written by S.K. Godunov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-06-30 with Computers categories.
There exists a vast literature on numerical methods of linear algebra. In our bibliography list, which is by far not complete, we included some monographs on the subject [46], [15], [32], [39], [11], [21]. The present book is devoted to the theory of algorithms for a single problem of linear algebra, namely, for the problem of solving systems of linear equations with non-full-rank matrix of coefficients. The solution of this problem splits into many steps, the detailed discussion of which are interest ing problems on their own (bidiagonalization of matrices, computation of singular values and eigenvalues, procedures of deflation of singular values, etc. ). Moreover, the theory of algorithms for solutions of the symmetric eigenvalues problem is closely related to the theory of solv ing linear systems (Householder's algorithms of bidiagonalization and tridiagonalization, eigenvalues and singular values, etc. ). It should be stressed that in this book we discuss algorithms which to computer programs having the virtue that the accuracy of com lead putations is guaranteed. As far as the final program product is con cerned, this means that the user always finds an unambiguous solution of his problem. This solution might be of two kinds: 1. Solution of the problem with an estimate of errors, where abso lutely all errors of input data and machine round-offs are taken into account. 2.
Lectures On Finite Precision Computations
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Author : Francoise Chaitin-Chatelin
language : en
Publisher: SIAM
Release Date : 1996-01-01
Lectures On Finite Precision Computations written by Francoise Chaitin-Chatelin and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-01 with Mathematics categories.
Finite precision computations are at the heart of the daily activities of many engineers and researchers in all branches of applied mathematics. Written in an informal style, the book combines techniques from engineering and mathematics to describe the rigorous and novel theory of computability in finite precision. In the challenging cases of nonlinear problems, theoretical analysis is supplemented by software tools to explore the stability on the computer.
Numerical Linear Algebra And Applications
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Author : Biswa Nath Datta
language : en
Publisher: SIAM
Release Date : 2010-01-01
Numerical Linear Algebra And Applications written by Biswa Nath Datta and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-01 with Mathematics categories.
Full of features and applications, this acclaimed textbook for upper undergraduate level and graduate level students includes all the major topics of computational linear algebra, including solution of a system of linear equations, least-squares solutions of linear systems, computation of eigenvalues, eigenvectors, and singular value problems. Drawing from numerous disciplines of science and engineering, the author covers a variety of motivating applications. When a physical problem is posed, the scientific and engineering significance of the solution is clearly stated. Each chapter contains a summary of the important concepts developed in that chapter, suggestions for further reading, and numerous exercises, both theoretical and MATLAB and MATCOM based. The author also provides a list of key words for quick reference. The MATLAB toolkit available online, 'MATCOM', contains implementations of the major algorithms in the book and will enable students to study different algorithms for the same problem, comparing efficiency, stability, and accuracy.
Numerical Linear Algebra
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Author : SUNDARAPANDIAN, V.
language : en
Publisher: PHI Learning Pvt. Ltd.
Release Date : 2008-04-23
Numerical Linear Algebra written by SUNDARAPANDIAN, V. and has been published by PHI Learning Pvt. Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-23 with Mathematics categories.
This well-organized text provides a clear analysis of the fundamental concepts of numerical linear algebra. It presents various numerical methods for the basic topics of linear algebra with a detailed discussion on theory, algorithms, and MATLAB implementation. The book provides a review of matrix algebra and its important results in the opening chapter and examines these results in the subsequent chapters. With clear explanations, the book analyzes different kinds of numerical algorithms for solving linear algebra such as the elimination and iterative methods for linear systems, the condition number of a matrix, singular value decomposition (SVD) of a matrix, and linear least-squares problem. In addition, it describes the Householder and Givens matrices and their applications, and the basic numerical methods for solving the matrix eigenvalue problem. Finally, the text reviews the numerical methods for systems and control. Key Features Includes numerous worked-out examples to help students grasp the concepts easily. Provides chapter-end exercises to enable students to check their comprehension of the topics discussed. Gives answers to exercises with hints at the end of the book. Uses MATLAB software for problem-solving. Primarily designed as a textbook for postgraduate students of Mathematics, this book would also serve as a handbook on matrix computations for scientists and engineers.
Accuracy And Stability Of Numerical Algorithms
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Author : Nicholas J. Higham
language : en
Publisher: SIAM
Release Date : 2002-01-01
Accuracy And Stability Of Numerical Algorithms written by Nicholas J. Higham and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.
Accuracy and Stability of Numerical Algorithms gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. This second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing LU factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures.
Applied Numerical Linear Algebra
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Author : James W. Demmel
language : en
Publisher: SIAM
Release Date : 1997-08-01
Applied Numerical Linear Algebra written by James W. Demmel and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-01 with Mathematics categories.
This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.
Error Control And Adaptivity In Scientific Computing
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Author : Haydar Bulgak
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Error Control And Adaptivity In Scientific Computing written by Haydar Bulgak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
One of the main ways by which we can understand complex processes is to create computerised numerical simulation models of them. Modern simulation tools are not used only by experts, however, and reliability has therefore become an important issue, meaning that it is not sufficient for a simulation package merely to print out some numbers, claiming them to be the desired results. An estimate of the associated error is also needed. The errors may derive from many sources: errors in the model, errors in discretization, rounding errors, etc. Unfortunately, this situation does not obtain for current packages and there is a great deal of room for improvement. Only if the error can be estimated is it possible to do something to reduce it. The contributions in this book cover many aspects of the subject, the main topics being error estimates and error control in numerical linear algebra algorithms (closely related to the concept of condition numbers), interval arithmetic and adaptivity for continuous models.
Iterative Methods For Solving Nonlinear Equations And Systems
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Author : Juan R. Torregrosa
language : en
Publisher: MDPI
Release Date : 2019-12-06
Iterative Methods For Solving Nonlinear Equations And Systems written by Juan R. Torregrosa and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-06 with Mathematics categories.
Solving nonlinear equations in Banach spaces (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others), is a non-trivial task that involves many areas of science and technology. Usually the solution is not directly affordable and require an approach using iterative algorithms. This Special Issue focuses mainly on the design, analysis of convergence, and stability of new schemes for solving nonlinear problems and their application to practical problems. Included papers study the following topics: Methods for finding simple or multiple roots either with or without derivatives, iterative methods for approximating different generalized inverses, real or complex dynamics associated to the rational functions resulting from the application of an iterative method on a polynomial. Additionally, the analysis of the convergence has been carried out by means of different sufficient conditions assuring the local, semilocal, or global convergence. This Special issue has allowed us to present the latest research results in the area of iterative processes for solving nonlinear equations as well as systems and matrix equations. In addition to the theoretical papers, several manuscripts on signal processing, nonlinear integral equations, or partial differential equations, reveal the connection between iterative methods and other branches of science and engineering.
Spectra And Pseudospectra
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Author : Lloyd N. Trefethen
language : en
Publisher: Princeton University Press
Release Date : 2020-05-05
Spectra And Pseudospectra written by Lloyd N. Trefethen and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-05 with Mathematics categories.
Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in. This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.