Numerical Matrix Analysis: Linear Systems and Least Squares

Contents: Preface. Introduction. 1 Matrices. 2 Sensitivity, Errors, and Norms. 3 Linear Systems. 4 Singular Value Decomposition. 5 Least Squares Problems. 6 Subspaces. Index. 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 readersÕ understanding of two phenomena: sensitivity of linear systems and least squares problems, and numerical stability of algorithms. 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, 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 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.…