Fully Symmetric Interpolatory Rules for Multiple Integrals over Innnite Regions with Gaussian Weight
نویسنده
چکیده
Fully symmetric interpolatory integration rules are constructed for multidimensional inte-grals over innnite integration regions with a Gaussian weight function. The points for these rules are determined by successive extensions of the one dimensional three point Gauss-Hermite rule. The new rules are shown to be eecient and only moderately unstable.
منابع مشابه
Fully Symmetric Interpolatory Rules for Multiple Integrals over Infinite Regions with Gaussian Weight
Fully symmetric interpolatory integration rules are constructed for multidimensional integrals over infinite integration regions with a Gaussian weight function. The points for these rules are determined by successive extensions of the one dimensional three point GaussHermite rule. The new rules are shown to be efficient and only moderately unstable.
متن کاملA Stochastic Algorithm for High Dimensional Integrals over Unbounded Regions with Gaussian Weight
Details are given for a Fortran implementation of an algorithm that uses stochastic spherical-radial rules for the numerical computation of multiple integrals over unbounded regions with Gaussian weight. The implemented rules are suitable for high dimensional problems. A high dimensional example from a computational nance application is used to illustrate the use of the rules.
متن کاملStochastic Integration Rules forIn nite Regions
Stochastic integration rules are derived for innnite integration intervals, generalizing rules developed by Siegel and O'Brien (1985) for nite intervals. Then random orthogonal transformations of rules for integrals over the surface of the unit m-sphere are used to produce stochastic rules for these integrals. The two types of rules are combined to produce stochastic rules for multidimensional ...
متن کاملOn the Convergence of an Interpolatory Product Rule for Evaluating Cauchy Principal Value Integrals*
The authors give convergence theorems for interpolatory product rules for evaluating Cauchy singular integrals and obtain asymptotic estimates of the remainder. Some results, previously established by other authors, are generalized and improved.
متن کاملBiorthogonal polynomials and numerical quadrature formulas for some finite-range integrals with symmetric weight functions
MSC: 41A55 41A60 65B05 65B10 65B15 65D30 Keywords: Biorthogonal polynomials Numerical integration Symmetric weight functions Acceleration of convergence Levin transformation Rational approximation a b s t r a c t In this work, we derive a family of symmetric numerical quadrature formulas for finite-range integrals I[f ] = 1 −1 w(x)f (x) dx, where w(x) is a symmetric weight function. In partic...
متن کامل