Numerical Methods in Scientific Computing

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.