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Numerical Matrix Analysis: Linear Systems and Least Squares

Numerical Matrix Analysis: Linear Systems and Least Squares

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Numerical Matrix Analysis: Linear Systems and Least Squares

Numerical Matrix Analysis: Linear Systems and Least Squares Summary:

 
By Ilse C. F. Ipsen
  • Publisher:   Society for Industrial and Applied Mathematics
  • Number Of Pages:   142
  • Publication Date:   2009-07-02
  • ISBN-10 / ASIN:   0898716764
  • ISBN-13 / EAN:   9780898716764
Product Description:

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 rigor, 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.

Audience:

This book is intended for first-year graduate students in engineering, operations research, computational science, and all areas of mathematics. It also is appropriate for self-study.

Contents:

Preface

Introduction

Chapter 1: Matrices
Chapter 2: Sensitivity, Errors, and Norms
Chapter 3: Linear Systems
Chapter 4: Singular Value Decomposition
Chapter 5: Least Square Problems
Chapter 6: Subspaces

Index

 

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