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Froberg C.-E. Introduction to Numerical Analysis

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Froberg C.-E. Introduction to Numerical Analysis
Addison-Wesley Publishing Company, 1969. — 443 p.
The present text in numerical analysis was written primarily to meet the demand of elementary education in this field at universities and technical institutes. But it is also believed that the book will be useful as a handbook in connection with numerical work within natural and technical sciences. Compared with the first edition a thorough revision and modernization has been performed, and quite a few new topics have been introduced. Two completely new chapters, integral equations and special functions, have been appended. Major changes and additions have been made, especially in Chapters 6, 14, and 15, while minor changes appear in practically all the remaining chapters. In this way the volume of the book has increased by about 30%.
An introductory text must have a two-fold purpose: to describe different numerical methods technically, as a rule in connection with the derivation of the methods, but also to analyze the properties of the methods, particularly with respect to convergence and error propagation. It is certainly not an easy task to achieve a reasonable balance on this point. On one hand, the book must not degenerate into a collection of recipes; on the other, the description should not be flooded by complete mathematical analyses of every trivial method. Actually, the text is not written in a hard-boiled mathematical style; however, this does not necessarily imply a lack of stringency. For really important and typical methods a careful analysis of errors and of error propagation has been performed. This is true especially for the chapters on linear systems of equations, eigenvalue problems, and ordinary and partial differential equations. Any person who has worked on numerical problems within these sectors is familiar with the feeling of uncertainty as to the correctness of the result which often prevails in such cases, and realistic and reliable error estimations are naturally highly desirable. In many situations, however, there might also be other facts available indicating how trustworthy the results are.
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