Numerical Matrix Analysis

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. It uses a unique combination of numerical insight and mathematical rigour. 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.