Excellent advanced-undergraduate and graduate text covers norms, numerical solution of linear systems and matrix factoring, iterative solutions of nonlinear equations, eigenvalues and eigenvectors, polynomial approximation and more. Careful analysis and stress on techniques for developing new methods. Features examples and problems. 1966 edition. Bibliography.
This edition contains minor corrections to the original edition. In the 28 years that have elapsed between these two editions, there have been great changes in computing equipment and in the development of numerical methods. However, the analysis required to understand and to devise new methods has not changed, and, thus, this somewhat mature text is still relevant. To the list of important tOpiCS omitted in the original edition (namely, linear programming, rational approximation and Monte Carlo) we must now add fast transforms, finite elements, wavelets, complexity theory, multigrid methods, adaptive gridding, path following and parallel algorithms. Hopefully, some energetic young numerical analyst will incorporate all these missing topics into an updated version to aid the burgeoning field of scientific computing.
We thank the many people who have pointed out errors and misprints in the original edition. In particular, Mr. Carsten Elsner suggested an elegant improvement in our demonstration of the Runge phenomenon, which we have adopted in Problem 8 on page 280.