Dahlquist G., Björck Ǻ. Numerical Methods

Mineola: Dover Publications. – 2003. – 594 p. — (Dover Books on Mathematics).This book is an extended and updated translation of a textbook published in Swedish by the CWK Gleerup Co. in 1969. Prerequisites for most of the book are sophomore courses in mathematics (in particular calculus and linear algebra) as well as some knowledge of a problem-oriented programming language. The latter can be studied in parallel with the first three chapters of the book. Parts of the book are more difficult. We hope that it will be easy for teachers who will use the book as a text to give instructions as to what depth the various parts are to be studied in a particular course. We have tried to select methods which are important to large-scale computing as well as techniques for small-scale computing with simple tools. It is helpful if the reader has access to a time-sharing system for getting acquainted with some of the algorithms, though in most cases a desk calculator or even a slide rule and mathematical tables can be useful enough. We hope that the book will be useful as a handbook for computation in science and technology. The last chapter contains an extensive bibliography and a list of published algorithms. The general ideas and concepts of scientific computation are introduced in the first chapter, while the second chapter is devoted to error analysis. There and everywhere else we try to stress those aspects which are of importance for the design of algorithms. In contrast to the general survey style of the first two chapters, the rest of the book is mostly concerned with the treatment of various classes of problems.Conventions.
Some general principles of numerical calculation.
How to obtain and estimate accuracy in numerical calculations.
Numerical uses of series.
Approximation of functions.
Numerical linear algebra.
Nonlinear equations.
Finite differences with applications to numerical integration, differentiation, and interpolation.
Differential equations.
Fourier methods.
Optimization.
The Monte Carlo method and simulation.
Solutions to problems bibliography and published algorithms.
Index by Subject to Algorithms, 1960-1970.
Appendix tables.