Numerical Methods that Work

Front Cover
MAA, 1990 - Mathematics - 549 pages
Numerical Methods that Work, originally published in 1970, has been reissued by the MAA with a new preface and some additional problems. Acton deals with a commonsense approach to numerical algorithms for the solution of equations: algebraic, transcendental, and differential. He assumes that a computer is available for performing the bulk of the arithmetic. The book is divided into two parts, either of which could form the basis of a one-semester course in numerical methods. Part I discusses most of the standard techniques: roots of transcendental equations, roots of polynomials, eigenvalues of symmetric matrices, and so on. Part II cuts across the basic tools, stressing such commonplace problems as extrapolation, removal of singularities, and loss of significant figures. The book is written with clarity and precision, intended for practical rather than theoretical use. This book will interest mathematicians, both pure and applied, as well as any scientist or engineer working with numerical problems.
 

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Contents

THE CALCULATION OF FUNCTIONS
5
ROOTS OF TRANSCENDENTAL EOUATIONS
41
INTERPOLATION AND ALL THAT
89
OUADRATURE
100
ORDINARY DIFFERENTIAL EOUATIONS
129
solved We then solve a slightly nonlinear differential equation
134
ORDINARY DIFFERENTIAL EOUATIONS
157
STRATEGY VERSUS TACTICS
178
ECONOMIZATION OF APPROXIMATIONS
289
EIGENVALUES IIROTATIONAL METHODS
316
ROOTS OF EOUATIONSAGAIN
361
THE CARE AND TREATMENT
410
INSTABILITY IN EXTRAPOLATION
431
MINIMUM METHODS
448
An exposition of some of the more effective ways to find
463
NETWORK PROBLEMS
499

EIGENVALUES I
204
FOURIER SERIES
221
THE EVALUATION OF INTEGRALS
261
POWER SERIES CONTINUED FRACTIONS
279
AFTERTHOUGHTS
529
BIBLIOGRAPHY
537
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