Introduction to Numerical Analysis: v. 12 (Texts in Applied Mathematics) - Hardcover

Stoer, Josef; Bulirsch, Roland

Hardcover

ISBN 10: 354097878X ISBN 13: 9783540978787

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1992

Synopsis

This second edition is the English translation of a text that 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 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 discussions of various algorithms, fully worked-out examples, and many formulated and selected problems. The text contains a 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 also 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.

About this title

Review

From the reviews of the third edition:

"This is the third edition of a famous work on the basics of numerical analysis. It is a well-written textbook for advanced undergraduate/beginning graduate students containing both classical methods and modern approaches to numerical mathematics. The theory is illustrated by many interesting examples, and carefully selected exercises lead the reader to a better understanding of the topics discussed. ... The third edition contains new material and several improved passages and will be useful also for those who already use the previous editions." (European Mathematical Society Newsletter, September, 2003)

"This is the third edition of a textbook first published in 1980. It is intended as a comprehensive introduction to ... numerical analysis for the final year undergraduate or beginning graduate student. ... As a reference work it is clearly organized and the table of contents ... makes it easier to refer to individual sections. ... it will serve both as an invaluable reference and as a means to acquire some more theoretical background ... ." (Gerry Leversha, The Mathematical Gazette, Vol. 88 (512), 2004)

"Among the book’s many particular features ... we would like to emphasize the excellent presentation of the following topics: fast Fourier transform methods, thorough discussion of the most important minimization methods, solution of stiff or implicit ordinary differential equations, solution of differential algebraic systems, basics of multigrid methods. ... This ... makes the present well-written book very profitable for every reader interested in or working on problems of Numerical Analysis." (Ferenc Móricz, Acta Scientiarum Mathematicarum, Vol. 69, 2003)

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 1992
• ISBN 10: 354097878X
• ISBN 13: 9783540978787
• Binding: Hardcover
• Language: German
• Edition number: 2
• Number of pages: 673