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The Numerical Jordan Form

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The Numerical Jordan Form

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Author : Petko H Petkov
language : en
Publisher: World Scientific
Release Date : 2024-05-24

The Numerical Jordan Form written by Petko H Petkov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-24 with Mathematics categories.

The Numerical Jordan Form is the first book dedicated to exploring the algorithmic and computational methods for determining the Jordan form of a matrix, as well as addressing the numerical difficulties in finding it. Unlike the 'pure' Jordan form, the numerical Jordan form preserves its structure under small perturbations of the matrix elements so that its determination presents a well-posed computational problem. If this structure is well conditioned, it can be determined reliably in the presence of uncertainties and rounding errors.This book addresses the form's application in solving some important problems such as the estimation of eigenvalue sensitivity and computing the matrix exponential. Special attention is paid to the Jordan-Schur form of a matrix which, the author suggests, is not exploited sufficiently in the area of matrix computations. Since the mathematical objects under consideration can be sensitive to changes in the elements of the given matrix, the book also investigates the perturbation analysis of eigenvalues and invariant subspaces. This study is supplemented by a collection over 100 M-files suitable for MATLAB in order to implement the state-of-the art algorithms presented in the book for reducing a square matrix into the numerical Jordan form.Researchers in the fields of numerical analysis and matrix computations and any scientists who utilise matrices in their work will find this book a useful resource, and it is also a suitable reference book for graduate and advance undergraduate courses in this subject area.

The Numerical Jordan Form

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Author : Petko H Petkov
language : en
Publisher: World Scientific Publishing Company
Release Date : 2024-07-14

The Numerical Jordan Form written by Petko H Petkov and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-14 with Mathematics categories.

Numerical Methods For Large Eigenvalue Problems

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Author : Yousef Saad
language : en
Publisher: SIAM
Release Date : 2011-05-26

Numerical Methods For Large Eigenvalue Problems written by Yousef Saad and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-26 with Mathematics categories.

This revised edition discusses numerical methods for computing the eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method and automatic multilevel substructuring.

Introduction To Precise Numerical Methods

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Author : Oliver Aberth
language : en
Publisher: Elsevier
Release Date : 2007-04-11

Introduction To Precise Numerical Methods written by Oliver Aberth and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-11 with Mathematics categories.

Precise numerical analysis may be defined as the study of computer methods for solving mathematical problems either exactly or to prescribed accuracy. This book explains how precise numerical analysis is constructed. The book also provides exercises which illustrate points from the text and references for the methods presented. - Clearer, simpler descriptions and explanations of the various numerical methods - Two new types of numerical problems; accurately solving partial differential equations with the included software and computing line integrals in the complex plane

A Graduate Introduction To Numerical Methods

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Author : Robert M. Corless
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-12

A Graduate Introduction To Numerical Methods written by Robert M. Corless 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 2013-12-12 with Mathematics categories.

This book provides an extensive introduction to numerical computing from the viewpoint of backward error analysis. The intended audience includes students and researchers in science, engineering and mathematics. The approach taken is somewhat informal owing to the wide variety of backgrounds of the readers, but the central ideas of backward error and sensitivity (conditioning) are systematically emphasized. The book is divided into four parts: Part I provides the background preliminaries including floating-point arithmetic, polynomials and computer evaluation of functions; Part II covers numerical linear algebra; Part III covers interpolation, the FFT and quadrature; and Part IV covers numerical solutions of differential equations including initial-value problems, boundary-value problems, delay differential equations and a brief chapter on partial differential equations. The book contains detailed illustrations, chapter summaries and a variety of exercises as well some Matlab codes provided online as supplementary material. “I really like the focus on backward error analysis and condition. This is novel in a textbook and a practical approach that will bring welcome attention." Lawrence F. Shampine A Graduate Introduction to Numerical Methods and Backward Error Analysis” has been selected by Computing Reviews as a notable book in computing in 2013. Computing Reviews Best of 2013 list consists of book and article nominations from reviewers, CR category editors, the editors-in-chief of journals, and others in the computing community.

Numerical Methods In Matrix Computations

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Author : Åke Björck
language : en
Publisher: Springer
Release Date : 2014-10-07

Numerical Methods In Matrix Computations written by Åke Björck and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-07 with Mathematics categories.

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.

Numerical Algorithms

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Author : Justin Solomon
language : en
Publisher: CRC Press
Release Date : 2015-06-24

Numerical Algorithms written by Justin Solomon and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-24 with Computers categories.

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

Precise Numerical Methods Using C

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Author : Oliver Aberth
language : en
Publisher: Academic Press
Release Date : 1998

Precise Numerical Methods Using C written by Oliver Aberth and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Computers categories.

This book explains how precise numerical analysis is constructed with C++. Included is a CD-ROM which contains executable Windows 95 programs for the PC and which demonstrates how these programs can be used to solvetypical problems of elementary numerical analysis with precision. The book also provides exercises which illustrate points from the text and references for the methods presented.

Stability And Stabilization

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Author : William J. Terrell
language : en
Publisher: Princeton University Press
Release Date : 2009-02-15

Stability And Stabilization written by William J. Terrell 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 2009-02-15 with Mathematics categories.

Stability and Stabilization is the first intermediate-level textbook that covers stability and stabilization of equilibria for both linear and nonlinear time-invariant systems of ordinary differential equations. Designed for advanced undergraduates and beginning graduate students in the sciences, engineering, and mathematics, the book takes a unique modern approach that bridges the gap between linear and nonlinear systems. Presenting stability and stabilization of equilibria as a core problem of mathematical control theory, the book emphasizes the subject's mathematical coherence and unity, and it introduces and develops many of the core concepts of systems and control theory. There are five chapters on linear systems and nine chapters on nonlinear systems; an introductory chapter; a mathematical background chapter; a short final chapter on further reading; and appendixes on basic analysis, ordinary differential equations, manifolds and the Frobenius theorem, and comparison functions and their use in differential equations. The introduction to linear system theory presents the full framework of basic state-space theory, providing just enough detail to prepare students for the material on nonlinear systems. Focuses on stability and feedback stabilization Bridges the gap between linear and nonlinear systems for advanced undergraduates and beginning graduate students Balances coverage of linear and nonlinear systems Covers cascade systems Includes many examples and exercises

Explorations In Numerical Analysis Python Edition

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Author : James V Lambers
language : en
Publisher: World Scientific
Release Date : 2021-01-14

Explorations In Numerical Analysis Python Edition written by James V Lambers and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-14 with Mathematics categories.

This textbook is intended to introduce advanced undergraduate and early-career graduate students to the field of numerical analysis. This field pertains to the design, analysis, and implementation of algorithms for the approximate solution of mathematical problems that arise in applications spanning science and engineering, and are not practical to solve using analytical techniques such as those taught in courses in calculus, linear algebra or differential equations.Topics covered include computer arithmetic, error analysis, solution of systems of linear equations, least squares problems, eigenvalue problems, nonlinear equations, optimization, polynomial interpolation and approximation, numerical differentiation and integration, ordinary differential equations, and partial differential equations. For each problem considered, the presentation includes the derivation of solution techniques, analysis of their efficiency, accuracy and robustness, and details of their implementation, illustrated through the Python programming language.This text is suitable for a year-long sequence in numerical analysis, and can also be used for a one-semester course in numerical linear algebra.

The Numerical Jordan Form

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