附註:Includes bibliographical references (pages 627-641) and indexes.
Cover -- Preface -- Table of Contents -- 1. Foundations of Matrix Analysis -- 2. Principles of Numerical Mathematics -- 3. Direct Methods for the Solution of Linear Systems -- 4. Iterative Methods for Solving Linear Systems -- 5. Approximation of Eigenvalues and Eigenvectors -- 6. Root -- 7. Nonlinear Systems and Numerical Optimization -- 8. Polynomial Interpolation -- 9. Numerical Integration -- 10. Orthogonal Polynomials in Approximation Theory -- 11. Numerical Solution of Ordinary Differential Equations -- 12. Two-Point Boundary Value Problems -- 13. Parabolic and Hyperbolic Initial Boundary Value Problems -- References -- Index of MATLAB Programs.
摘要:"One of the purposes of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties (stability, accuracy, and computational complexity), and to demonstrate their performances on examples and counterexamples, which outline their pros and cons. This is done using the MATLAB software environment, which is user-friendly and widely adopted. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out, and the expected results are verified on a MATLAB computer implementation. Every chapter is supplied with examples, exercises, and applications of the discussed theory to the solution of real-life problems." "This book is addressed to senior undergraduate and graduate students with particular focus on degree courses in engineering, mathematics, physics, and computer science. The attention paid to the applications and the related development of software makes it valuable also to researchers and users of scientific computing in a large variety of professional fields."--Jacket
