Methods of Numerical Integration
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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abscissas abscissas and weights accuracy adaptive algorithm Anal analytic functions applied approximate integration automatic integration bounded CACM Cauchy principal value coefﬁcients Comp computation convergence cubature deﬁned deﬁnition degree derivatives differential equations dimensions Doncker error estimate example fast Fourier transform ﬁgures ﬁnd ﬁnite ﬁrst ﬁxed Fourier transform function evaluations function f Gauss rule Gaussian quadrature Genz given Hence hypercube indeﬁnite integral inner product integrand integration formulas integration rule interpolation interpolatory Krylov Laguerre Laplace transform linear Lobatto Lyness Math method modiﬁed monomials multiple integrals Newton—Cotes norm number of functional number of points numerical integration numerical quadrature obtain orthogonal polynomials oscillatory Phys Piessens quadrature formulas Rabinowitz References region Riemann integral Romberg Romberg integration roundoff satisﬁes Section sequence SIAM Simpson’s rule singularity spline subintervals sufﬁciently symmetric theorem theory trapezoidal rule Tschebyscheff variable weight function zeros