Methods of Numerical IntegrationCourier Corporation, 1 janv. 2007 - 612 pages Useful to programmers and stimulating for theoreticians, this text covers the major methods of numerical integration. It offers a balanced presentation: certain sections derive from or allude to deep results of analysis, but most of the final results are expressed in a form accessible to anyone with a background in calculus. An extensive introduction outlines the uses and advantages of numerical integration and includes formulas and guides to orthogonal polynomials and specific integrals. Subsequent chapters explore approximate integration over finite and infinite intervals, error analysis, approximate integration in two or more dimensions, and automatic integration. Five helpful appendixes conclude the text. |
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Expressions et termes fréquents
a₁ abscissas abscissas and weights accuracy adaptive algorithm Anal analytic functions applied approximate integration asymptotic automatic integration bounded CACM Cauchy principal value Clenshaw-Curtis coefficients Comp computation convergence cubature defined derivatives differential equations dimensions Doncker dx dy error estimate example expansion finite Fourier transform function f functional evaluations Gauss rule Gaussian quadrature Genz given Hence hypercube indefinite integral inner product integrand integration formulas integration rule interpolation interpolatory interval Krylov Laguerre Laplace transform linear Lobatto Lyness Math method monomials multiple integrals Newton-Cotes number of functional number of points numerical integration numerical quadrature obtain orthogonal polynomials oscillatory Phys Piessens quadrature formulas Rabinowitz References Riemann integral Romberg Romberg integration roundoff Section sequence SIAM Simpson's rule singularity spline subintervals theorem trapezoidal rule Tschebyscheff variable w₁ weight function x₁ zeros