Numerical linear algebra

Author: Xu Shufang
Publisher:
Publish Date: 2000-09-01
Features: This book is a textbook for undergraduate students majoring in computational mathematics in university mathematics departments. The book is divided into 8 chapters, covering the following content: Introduction, Gauss elimination method, square root method, classical iterative method, and conjugate gradient method for solving linear equations, sensitivity analysis of linear equation systems and rounding error analysis of elimination methods, orthogonal decomposition method for solving linear least squares problems, power method, inverse power method, Jacobi method, bisection method, divide and conquer method, and QR method for solving matrix eigenvalue problems. The book emphasizes both fundamental knowledge and practicality in its selection of materials, while also reflecting the latest developments in the field. In terms of content presentation, it explains the design ideas and theoretical foundations of the methods as much as possible, and provides rigorous yet concise pedagogical proofs for relevant conclusions. The writing style aims to be clear and readable, facilitating both teaching and self-study. Each chapter is accompanied by a rich set of exercises and computer-based problems, designed to provide students with sufficient practice and practical material to review, consolidate, and expand on the knowledge learned in class. This book can serve as a textbook or reference for undergraduate students in computational mathematics, applied mathematics, and engineering computation at comprehensive universities, universities of science and engineering, and advanced normal universities. It can also be used as a reference for scientists and engineers engaged in scientific and engineering computations.