Numerical analysis

Author: Lin Chengsen
Publisher:
Publish Date: 2007-01-01
Features: This book systematically introduces fundamental and commonly used numerical computation methods, as well as some modern numerical methods and relevant theoretical analyses. The main content includes direct and iterative methods for solving systems of linear equations, interpolation methods, function approximation, least squares fitting of data, numerical integration, numerical methods for solving nonlinear equations and systems of equations, numerical solutions for initial and boundary value problems of ordinary differential equations, numerical methods for finding the least squares solution of linear systems of equations, and matrix eigenvalue problems. In addition to introducing common numerical methods, the book also emphasizes the fundamental principles and theoretical analyses of numerical analysis, with rigorous, detailed, and easy-to-understand explanations. To enhance readers' understanding of the book's content, numerous examples are provided, and an adequate number of exercises are included at the end of each chapter. Solutions to most exercises are given at the end of the book, and hints are provided for most proof-based problems for reference. This book can serve as a textbook for students in mathematics, computer science, and other related disciplines at universities and colleges, as well as a reference for engineering professionals. The content of the book covers numerical computation errors, direct and iterative methods for solving systems of linear equations, least squares solutions of linear systems, matrix eigenvalue problems, interpolation methods, function approximation, curve fitting, numerical integration, and numerical methods for solving nonlinear equations and systems of equations. The book includes a wealth of examples and exercises of varying difficulty levels, and most algorithms are presented using pseudocode. This book is suitable for students in information and computation science, mathematics, applied mathematics, and computer application majors at general universities and colleges.