Datasets

type: dataset

Total is 1440 Results
OCVdM: Optimally conditioned Vandermonde matrices

10.4231/R7TB14TB

Walter Gautschi

04/23/2014

This software source code investigates numerically the extent to which the condition number of such matrices can be reduced, either by row-scaling or by optimal configurations of nodes. In the latter case we find empirically the condition of the optimally...

Computer Science Condition Numbers Guassian Quadrature Logarithmic weight functions Mathematics Matlab Orthogonal polynomials Singular value decomposition Software source code Vandermonde matrices Walter Gautschi Archives

HOGGRL: High-order generalized Gauss-Radau and Gauss-Lobatto Formulae for Jacobi and Laguerre weight functions

10.4231/R7G15XSQ

Walter Gautschi

04/23/2014

The generation of generalized Gauss–Radau and Gauss–Lobatto quadrature formulae by methods developed by us earlier breaks down in the case of Jacobi and Laguerre measures when the order of the quadrature rules becomes very large. The reason for this is und...

Computer Science High-order generalized Gauss–Radau and Gauss–Lobatto quadrature formulae Jacobi weight functions Laguerre weight functions Mathematics Matlab Orthogonal polynomials Software source code Walter Gautschi Archives

NUMINT: Numerical Integration over the square

10.4231/R7PK0D31

Walter Gautschi

04/23/2014

Tensor-product formulae based on one-dimensional Gaussian quadratures are developed for evaluating double integrals of the type indicated in the title. If the singularities occur only along the diagonal and the regular part of the integrand is a polynomial...

Aerodynamical drag coefficient Computer Science Gauss quadrature approximation Gaussian quadrature Mathematics Matlab Numerical integration over the square Orthogonal polynomials Quadrature and cubature formulas Software source code Walter Gautschi Archives Walter Gautschi Selected Works

SRJAC: Sub-range Jacobi polynomials

10.4231/R7JS9NCR

Walter Gautschi

04/23/2014

Orthogonal polynomials relative to the Jacobi weight function, but orthogonal on a strict subinterval of [-1, 1] are studied, in particular with regard to their numerical computation. Related Gaussian quadrature rules are also considered.

Computation of recurrence coefficients and special Gaussian quadrature rules Computer Science Gaussian quadrature Jacobi weight functions Mathematics Matlab Orthogonal polynomials Software source code Sub-range Jacobi polynomials Walter Gautschi Archives

RMOP: Repeated modifications of orthogonal polynomials

10.4231/R7F18WNB

Walter Gautschi

04/23/2014

Algorithms are developed for computing the coefficients in the three-term recurrence relation of repeatedly modified orthogonal polynomials, the modifications involving division of the orthogonality measure by a linear function with real or complex coeffic...

Computer Science Gaussian quadrature Gaussian quadrature of functions having poles Jacobi polynomials Logarithmic weight functions Mathematics Matlab Modification algorithms for orthogonal polynomials Numerical integrations Orthogonal polynomials Software source code Walter Gautschi Archives

HPGT: High-precision Gauss-Turan quadrature rules

10.4231/R71V5BW8

Walter Gautschi

04/23/2014

Matlab software are presented for generating Gauss–Turán quadrature rules for the Laguerre and Hermite weight functions to arbitrarily high accuracy. This is accomplished by the Newton–Kantorovich method, using initial approximations that are sufficiently...

Computer Science Gauss-type quadrature rules Hermite weight function Laguerre weight functions Mathematics Matlab Orthogonal polynomials Software source code Variable-precision arithmetic Walter Gautschi Archives

NEUTRAL: Neutralizing nearby singularities in numerical quadrature

10.4231/R75H7D6P

Walter Gautschi

04/23/2014

A method of “neutralization” is presented that significantly weakens, if not eliminates, a singularity close to, but outside, the interval of integration.

Computer Science Gaussian quadrature Mathematics Matlab nearby singularities Numerical quadrature Orthogonal polynomials Software source code Walter Gautschi Archives

OPQ: A Matlab suite of programs for generating orthogonal polynomials and related quadrature rules

10.4231/R7959FHP

Walter Gautschi

03/29/2017

    A suite of Matlab programs has been developed as part of the book "Orthogonal Polynomials: Computation and Approximation", Clarendon Press, Oxford, 2014. The package contains routines for generating orthogonal polynomials as well as routines dealing wi...

Computer Science Gauss-type quadrature rules Mathematics Matlab Modification algorithms for orthogonal polynomials Orthogonal polynomials Software source code Variable-precision arithmetic Walter Gautschi Archives

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