Introduction to Numerical Analysis

This second edition is the English translation of a text that had found wide acceptance in its original German version. Written for the advanced undergraduate and beginning graduate student, it treats numerical techniques which can readily be implemented on digital computers and which are proven to be useful and reliable for high speed computation. A combination of modern mathematical standards with an understanding of the needs of the applied computer scientist is one of the characteristic features of the text. Other features are careful discussions of various algorithms, fully worked out examples, and many carefully formulated and selected problems. Though the authors went to great length to make the book accessible to students, it contains an extensive discussion of minimization methods and direct methods for the solution of large systems of equations, much of which is not found in the standard textbook literature. The book includes numerous references to contemporary research literature. For this new edition, the text was enlarged by several new sections. Two sections on B-splines and their computation were added to the chapter on spline functions. As suggested by many readers, the authors supplemented the chapter on elimination methods by a section dealing with the solution of large sparse systems of linear equations. The chapter on eigenvalue problems was enlarged by a section on the Lanczos algorithm. In order to take account of the progress in the area of ordinary differential equations, a new section on implicit differential equations and differential-algebraic systems was added.