Modern numerical analysis

Author: Lin Xiaolin
Publisher:
Publish Date: 2004-09-01
Features: This book presents clear basic concepts, uses easy-to-understand language, and features rigorous theoretical analysis. The structure is arranged from simple to complex, with an emphasis on inspirational problem-solving, targeted examples, and practical applications. Each chapter includes a certain number of exercises for readers to practice. This book is suitable for postgraduate students in science and engineering disciplines at universities, as well as senior undergraduate students in mathematics, information and computing science, physics, computer science, and other fields. It can also serve as a reference for science and engineering computing professionals. The book provides a comprehensive introduction to commonly used numerical computation methods in modern science and engineering computing. It covers the basic theories of these methods and their applications in various engineering fields, as well as a brief analysis of their computational performance, stability, convergence, applicability, and advantages and disadvantages. The book is divided into nine chapters, including the research content of numerical methods and error analysis, direct and iterative methods for solving systems of linear equations, iterative methods for solving nonlinear equations (systems), numerical algorithms for matrix eigenvalues and eigenvectors, function interpolation, function approximation, numerical integration and differentiation, and numerical methods for solving initial and boundary value problems of ordinary differential equations.