Introduction to Numerical Analysis

This book contains a large amount of information not found in standard textbooks. Written for the advanced undergraduate/beginning graduate student, it combines the modern mathematical standards of numerical analysis with an understanding of the needs of the computer scientist working on practical applications. Included are numerous references to contemporary research literature.

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)

Inhalt
1 Error Analysis.- 2 Interpolation.- 3 Topics in Integration.- 4 Systems of Linear Equations.- 5 Finding Zeros and Minimum Points by Iterative Methods.- 6 Eigenvalue Problems.- 7 Ordinary Differential Equations.- 8 Iterative Methods for the Solution of Large Systems of Linear Equations. Additional Methods.- General Literature on Numerical Methods.