Fundamentals of Matrix Computations - Couverture rigide

Watkins, David S.

Couverture rigide

ISBN 10 : 0471614149 ISBN 13 : 9780471614142

Editeur : John Wiley and Sons (WIE), 1991

Synopsis

Book by Watkins David S

A propos du livre

Quatrième de couverture

This new, modernized edition provides a clear and thorough introduction to matrix computations, a key component of scientific computing

Retaining the accessible and hands–on style of its predecessor, Fundamentals of Matrix Computations, Third Edition thoroughly details matrix computations and the accompanying theory alongside the author′s useful insights. The book presents the most important algorithms of numerical linear algebra and helps readers to understand how the algorithms are developed and why they work.

Along with new and updated examples, the Third Edition features:

• A novel approach to Francis′ QR algorithm that explains its properties without reference to the basic QR algorithm
• Application of classical Gram–Schmidt with reorthogonalization
• A revised approach to the derivation of the Golub–Reinsch SVD algorithm
• New coverage on solving product eigenvalue problems
• Expanded treatment of the Jacobi–Davidson method
• A new discussion on stopping criteria for iterative methods for solving linear equations

Throughout the book, numerous new and updated exercises ranging from routine computations and verifications to challenging programming and proofs are provided, allowing readers to immediately engage in applying the presented concepts. The new edition also incorporates MATLAB to solve real–world problems in electrical circuits, mass–spring systems, and simple partial differential equations, and an index of MATLAB terms assists readers with understanding the basic concepts related to the software.

Fundamentals of Matrix Computations, Third Edition is an excellent book for courses on matrix computations and applied numerical linear algebra at the upper–undergraduate and graduate level. The book is also a valuable resource for researchers and practitioners working in the fields of engineering and computer science who need to know how to solve problems involving matrix computations.

Quatrième de couverture

A significantly revised and improved introduction to a critical aspect of scientific computation

Matrix computations lie at the heart of most scientific computational tasks. For any scientist or engineer doing large–scale simulations, an understanding of the topic is essential. Fundamentals of Matrix Computations, Second Edition explains matrix computations and the accompanying theory clearly and in detail, along with useful insights.

This Second Edition of a popular text has now been revised and improved to appeal to the needs of practicing scientists and graduate and advanced undergraduate students. New to this edition is the use of MATLAB for many of the exercises and examples, although the Fortran exercises in the First Edition have been kept for those who want to use them. This new edition includes:
∗ Numerous examples and exercises on applications including electrical circuits, elasticity (mass–spring systems), and simple partial differential equations
∗ Early introduction of the singular value decomposition
∗ A new chapter on iterative methods, including the powerful preconditioned conjugate–gradient method for solving symmetric, positive definite systems
∗ An introduction to new methods for solving large, sparse eigenvalue problems including the popular implicitly–restarted Arnoldi and Jacobi–Davidson methods

With in–depth discussions of such other topics as modern componentwise error analysis, reorthogonalization, and rank–one updates of the QR decomposition, Fundamentals of Matrix Computations, Second Edition will prove to be a versatile companion to novice and practicing mathematicians who seek mastery of matrix computation.

Détails de l'édition

• Éditeur: John Wiley and Sons (WIE)
• Date d'édition: 1991
• ISBN 10: 0471614149
• ISBN 13: 9780471614142
• Reliure: Relié
• Langue: anglais
• Nombre de pages: 464