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Quadpack

A Subroutine Package for Automatic Integration

R. Piessens, E. de Doncker-Kapenga, C.W. Überhuber, D.K. Kahaner (Autoren)

Buch | Softcover

VIII, 304 Seiten

1983 | 1. Softcover reprint of the original 1st ed. 1983
Springer Berlin (Verlag)
978-3-540-12553-2 (ISBN)

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1. 1. Overview of Numerical Quadrature The numerical evaluation of integrals is one of the oldest problems in mathematics. One can trace its roots back at least to Archimedes. The task is to compute the value of the definite integral of a given function. This is the area under a curve in one dimension or a volume in several dimensions. In addition to being a problem of great practi cal interest it has also lead to the development of mathematics of much beauty and insight. Many portions of approximation theory are directly applicable to integration and results from areas as diverse as orthogo nal polynomials, Fourier series and number theory have had important implications for the evaluation of integrals. We denote the problem addressed here as numerical integration or numerical quadrature. Over the years analysts and engineers have contributed to a growing body of theorems, algorithms and lately, programs, for the solution of this specific problem. Much effort has been devoted to techniques for the analytic evalua tion of integrals. However, most routine integrals in practical scien tific work are incapable of being evaluated in closed form. Even if an expression can be derived for the value of an integral, often this reveals itself only after inordinate amounts of error prone algebraic manipulation. Recently some computer procedures have been developed which can perform analytic integration when it is possible.

I. Introduction.- II. Theoretical Background.- 2.1. Automatic integration with QUADPACK.- 2.2. Integration methods.- III. Algorithm Descriptions.- 3.1. QUADPACK contents.- 3.2. Prototype of algorithm description.- 3.3. Algorithm schemes.- 3.4. Heuristics used in the algorithms.- IV. Guidelines for the use of Quadpack.- 4.1. General remarks.- 4.2. Decision tree for finite-range integration.- 4.3. Decision tree for infinite-range integration.- 4.4. Numerical examples.- 4.5. Sample programs illustrating the use of the QUADPACK integrators.- V. Special Applications of Quadpack.- 5.1. Two-dimensional integration.- 5.2. Hankel transform.- 5.3. Numerical inversion of the Laplace transform.- VI. Implementation Notes and Routine Listings.- 6.1. Implementation notes.- 6.2. Routine listings.- References.

Erscheint lt. Verlag	1.7.1983
Reihe/Serie	Springer Series in Computational Mathematics
Zusatzinfo	VIII, 304 p.
Verlagsort	Berlin
Sprache	englisch
Maße	152 x 229 mm
Gewicht	462 g
Themenwelt	Informatik ► Theorie / Studium ► Algorithmen
	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	algorithms • Numerical Integration • numerical quadrature • Numerische Integration • QUADPACK • Quadraturformeln
ISBN-10	3-540-12553-1 / 3540125531
ISBN-13	978-3-540-12553-2 / 9783540125532
Zustand	Neuware