Numerical Matrix Analysis

Ilse C.F. Ipsen

ISBN 10: 0898716764 / ISBN 13: 9780898716764

Published by Society for Industrial and Applied Mathematics,U.S., US, 2009

About this Item

This self-contained textbook presents matrix analysis in the context of numerical computation with numerical conditioning of problems and numerical stability of algorithms at the forefront. Using a unique combination of numerical insight and mathematical rigour, it advances readers' understanding of two phenomena: sensitivity of linear systems and least squares problems, and numerical stability of algorithms.This book differs in several ways from other numerical linear algebra texts. It offers 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. The material is presented at a basic level, emphasizing ideas and intuition, and each chapter offers simple exercises for use in the classroom and more challenging exercises for student practice.This book differs from other numerical linear algebra texts by offering:A systematic development of numerical conditioning. A simplified concept of numerical stability in exact arithmetic.Simple derivations.A high-level view of algorithms. Results for complex matrices.The material is presented at a basic level, emphasizing ideas and intuition, and each chapter offers simple exercises for use in the classroom and more challenging exercises for student practice.

Seller Inventory # LU-9780898716764

Bibliographic Details

• Title: Numerical Matrix Analysis
• Publisher: Society for Industrial and Applied Mathematics,U.S., US
• Publication Date: 2009
• Language: English
• ISBN 10: 0898716764
• ISBN 13: 9780898716764
• Binding: Paperback
• Condition: New
• Weight: 200 grams

About this title

Synopsis

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.

About the Author

Ilse Ipsen is Professor of Mathematics at North Carolina State University. She is the SIAM Vice President for Programs and a member of the editorial boards of SIAM Review, the SIAM Journal on Matrix Analysis and Applications, Numerische Mathematik, and Numerical Linear Algebra with Applications.