Addresses the increasingly-important role of numerical methods in science and engineering. While treating traditional and well-developed topics, it also emphasizes concepts and ideas of importance to the design of accurate and efficient algorithms with applications to scientific computing. Although this volume is self-contained, more comprehensive treatments of matrix computations will be given in a forthcoming volume. Numerical Methods in Scientific Computing, Volume I enriches the traditional content of interpolation, approximation, Fourier analysis, quadrature, and root-finding with other material that is rarely found in numerical analysis texts, such as interval arithmetic, elementary functions, operator series, convergence acceleration, and continued fractions. The authors also include review questions, problems, and computer exercises drawn from 40 years of teaching. More than 60 short biographical notes on mathematicians who have made significant contributions to numerical analysis illustrate the connections that pervade the discipline. A supplementary Website contains three appendices: an introduction to matrix computations; a description of Mulprec, a MATLAB (R) multiple precision package; and a guide to literature, algorithms, and software in numerical analysis.
Germund Dahlquist (1925-2005) founded the Department of Numerical Analysis at the Royal Institute of Technology in Stockholm, Sweden, in 1962. He was a pioneer in the field of numerical analysis, whose fundamental work on the solution of differential equations has been recognised by the International Germund Dahlquist Prize, awarded biennially by SIAM since 1995. Ake Bjorck is a professor in the Department of Mathematics at Linkoping University in Sweden.
List of Figures List of Tables List of Conventions Preface Chapter 1: Principles of Numerical Calculations Chapter 2: How to Obtain and Estimate Accuracy Chapter 3: Series, Operators, and Continued Fractions Chapter 4: Interpolation and Approximation Chapter 5: Numerical Integration Chapter 6: Solving Scalar Nonlinear Equations Bibliography Index Online Appendix A: Introduction to Matrix Computations Online Appendix B: A MATLAB Multiple Precision Package Online Appendix C: Guide to Literature.
An introductory graduate course in numerical analysis and for researchers who use numerical methods in science and engineering.
'This work is a monumental undertaking and represents the most comprehensive textbook survey of numerical analysis to date. It will be an important reference in the field for many years to come.' Nicholas J. Higham, University of Manchester
