This paper is concerned with the approximation of matrix functionals defined by a large, sparse or structured, symmetric definite matrix. These functionals are Stieltjes integrals with a measure supported on a compact real interval. Rational Gauss quadrature rules that are designed to exactly integrate Laurent polynomials with a fixed pole in the vicinity of the support of the measure may yield...

This paper introduces GAUSS a system for the automatic selection of quadrature routines in numerical computation. Given a problem in numerical integration and constraints on time and accuracy, GAUSS comes up with an efficient algorithm to solve it. It banks on a performance database of various algorithms and test problems, an automatic feature identification module and a knowledge methodology t...

Nyström method is a standard numerical technique to solve Fredholm integral equations of the second kind where integration kernel approximated using quadrature formula. Traditionally, rule used classical polynomial Gauss quadrature. Motivated by observation that given function can be better spline lower degree than single piece higher degree, in this work, we investigate use Gaussian rules for ...

A numerical method for the calculation of Bessel function integrals is proposed for trial functions with exponential type behavior and evaluated for functions with and without explicit exponential dependence. This method utilizes the integral representation of the Bessel function to recast the problem as a double integral; one of which is calculated with Gauss-Chebyshev quadrature while the oth...

Oscillatory integrals over fan-shaped regions widely exist in scattering analysis, and this paper proposes a new rapid calculation routine for them. In the routine, the concerned bivariate scattering oscillatory integral is reduced to the calculation of two univariate oscillatory integrals. One is calculated with the improved Levin quadrature method, and another is transformed to a non-oscillat...

This paper proposes an approach for high-order time integration within a multi-domain setting for timefractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to properly account for the history/memory part and how to perform the integration accurately. To address these issues, we propose a novel hybrid a...

in this paper, numerical spline-based differential quadrature is presented for solving the boundary and initial value problems, and its application is used to solve the fixed rectangular membrane vibration equation. for the time integration of the problem, the runge–kutta and spline-based differential quadrature methods have been applied. the runge–kutta method was unstable for solving the prob...

Approximations of matrix-valued functions of the form WT f(A)W , where A ∈ Rm×m is symmetric, W ∈ Rm×k , with m large and k m, has orthonormal columns, and f is a function, can be computed by applying a few steps of the symmetric block Lanczos method to A with initial block-vector W ∈ Rm×k . Golub and Meurant have shown that the approximants obtained in this manner may be considered block Gauss...

We analyze the consistency, stability, and convergence of an hp discontinuous Galerkin spectral element method of Kopriva [J. Comput. Phys., 128 (1996), pp. 475–488] and Kopriva, Woodruff, and Hussaini [Internat. J. Numer. Methods Engrg., 53 (2002), pp. 105–122]. The analysis is carried out simultaneously for acoustic, elastic, coupled elastic-acoustic, and electromagnetic wave propagation. Our...

Abstract. In this note, we give some estimates of the generalized quadrature formula of Gauss-Jacobi type for phi-preinvex functions.