A First Course in Numerical Methods is designed for students and researchers who seek practical knowledge of modern techniques in scientific computing. Avoiding encyclopedic and heavily theoretical exposition, the book provides an in-depth treatment of fundamental issues and methods, the reasons behind the success and failure of numerical software, and fresh and easy-to-follow approaches and techniques. The authors focus on current methods, issues, and software while providing a comprehensive theoretical foundation, enabling those who need to apply the techniques to successfully design solutions to nonstandard problems. The book also illustrates algorithms using the programming environment of MATLAB(R), with the expectation that the reader will gradually become proficient in it while learning the material covered in the book. A variety of exercises are provided within each chapter along with review questions aimed at self-testing. The book takes an algorithmic approach, focusing on techniques that have a high level of applicability to engineering, computer science, and industrial mathematics.
Uri Ascher is a Professor of Computer Science at the University of British Columbia in Vancouver, Canada. He has previously co-authored three other books, published by SIAM, as well as many research papers in the general area of numerical methods and their applications. He is a SIAM Fellow and a recipient of the CAIMS Research Prize. Chen Greif is an Associate Professor of Computer Science at the University of British Columbia in Vancouver, Canada. His research interests are in the field of scientific computing, with specialization in numerical linear algebra. He is currently an associate editor of the SIAM Journal on Scientific Computing.
List of figures; List of tables; Preface; 1. Numerical algorithms; 2. Roundoff errors; 3. Nonlinear equations in one variable; 4. Linear algebra background; 5. Linear systems: direct methods; 6. Linear least squares problems; 7. Linear systems: iterative methods; 8. Eigenvalues and singular values; 9. Nonlinear systems and optimization; 10. Polynomial interpolation; 11. Piecewise polynomial interpolation; 12. Best approximation; 13. Fourier transform; 14. Numerical differentiation; 15. Numerical integration; 16. Differential equations; Bibliography; Index.