C. T. Fike, "Computer Evaluation of Mathematical Functions"
1968 | pages: 238 | ISBN: 0131657208 | PDF | 29,6 mb
This book developed from lecture notes for a class that I have taught for several years at the IBM Systems Research Institute. This is an eight-week class on mathematical methods used in function evaluation routines for digital computers. So far as I know, this is the first textbook to contain all the main topics relevant to this subject. Indeed, much of the material was not available in books at all and could be found only in original papers and in the documentation of existing computer programs. As the reader can see, the topics included in the book make a varied and interesting assortment and would probably not be grouped together under any other heading.
A short course or seminar based on this book should fit nicely into almost any computer science curriculum. Besides being of special interest in computing, the material provides opportunities for students to employ techniques learned in other courses. Thus, in some exercises a numerical analysis student can exploit his knowledge of numerical methods for solving nonlinear equations. Similarly there are exercises in which a student can make use of his ability to program a language for algebraic manipulation (such as Formac). To be able to do some of the exercises properly, a student should be able to program in a language like Algol, Fortran, or PL/I, and should have access to a computer.
The mathematical level of the book is for the most part that of a junior or senior undergraduate mathematics student. My rule concerning inclusion of proofs was to omit all nonelementary proofs and to include elementary ones selectively. References to suitable sources are provided for proofs that had to be omitted. A few proofs for which there was no space in the text were also made into exercises.
Bibliographies appear at the ends of chapters. These bibliographies are, of course, not exhaustive. The relevant literature is already large and continues to grow rapidly. I included only those sources that I thought would be especially interesting or practically useful to readers.
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