4.7 Article

Averaged Gauss quadrature formulas: Properties and applications

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article Mathematics, Applied

Exactness of Quadrature Formulas

Lloyd N. Trefethen

Summary: The standard design principle for quadrature formulas is not always accurate in predicting the actual behavior in well-known cases like Newton-Cotes, Clenshaw-Curtis, Gauss-Legendre, and Gauss-Hermite quadrature. New results include interesting observations and theorems that show the performance of different types of quadrature formulas in specific situations.

SIAM REVIEW (2022)

Article Mathematics, Applied

Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the first kind

Dusan Lj. Djukic et al.

Summary: The study investigates whether generalized averaged Gauss quadrature formulas for modified Chebyshev measures of the first kind are internal and can be effectively applied to estimate errors in associated Gauss quadrature rules.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2021)

Article Mathematics, Applied

Estimating the error in matrix function approximations

Nasim Eshghi et al.

Summary: This paper focuses on computing approximations of matrix functions f(A)v for large symmetric matrices A, where evaluating f(A) directly is prohibitively expensive. By using the symmetric Lanczos process, a small symmetric tridiagonal matrix T-n is computed to approximate f(A)v, and an estimation of the error in the computed approximation is provided based on a novel approach inspired by Spalevi's technique for estimating errors in Gauss quadrature rules.

ADVANCES IN COMPUTATIONAL MATHEMATICS (2021)

Article Mathematics, Applied

A new representation of generalized averaged Gauss quadrature rules

Lothar Reichel et al.

Summary: This paper presents a new representation of the generalized averaged Gauss formulas that offers an attractive alternative to the (2l + 1)-node Gauss-Kronrod rule, which may not exist with 2l + 1 real nodes. The representation is cheaper to evaluate than the available representation.

APPLIED NUMERICAL MATHEMATICS (2021)

Article Mathematics, Applied

Internality of generalized averaged Gaussian quadrature rules and truncated variants for modified Chebyshev measures of the second kind

Dusan Lj Djukic et al.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2019)

Article Computer Science, Software Engineering

Generalized averaged Gauss quadrature rules for the approximation of matrix functionals

Lothar Reichel et al.

BIT NUMERICAL MATHEMATICS (2016)

Article Mathematics, Applied

Truncated generalized averaged Gauss quadrature rules

Dusan Lj. Djukic et al.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2016)

Article Mathematics, Applied

ITERATION-FREE COMPUTATION OF GAUSS-LEGENDRE QUADRATURE NODES AND WEIGHTS

I. Bogaert

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2014)

Article Mathematics, Applied

FAST AND ACCURATE COMPUTATION OF GAUSS-LEGENDRE AND GAUSS-JACOBI QUADRATURE NODES AND WEIGHTS

Nicholas Hale et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2013)

Article Mathematics, Applied

Modified anti-Gauss and degree optimal average formulas for Gegenbauer measure

A. I. Hascelik

APPLIED NUMERICAL MATHEMATICS (2008)

Article Mathematics, Applied

New quadrature formulas from conformal maps

Nicholas Hale et al.

SIAM JOURNAL ON NUMERICAL ANALYSIS (2008)

Article Mathematics, Applied

Is Gauss quadrature better than Clenshaw-Curtis?

Lloyd N. Trefethen

SIAM REVIEW (2008)

Article Mathematics, Applied

The kink phenomenon in Fejer and Clenshaw-Curtis quadrature

J. A. C. Weideman et al.

NUMERISCHE MATHEMATIK (2007)

Article Mathematics, Applied

On generalized averaged Gaussian formulas

Miodrag M. Spalevic

MATHEMATICS OF COMPUTATION (2007)

Article Mathematics, Applied

A fast algorithm for the calculation of the roots of special functions

Andreas Glaser et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2007)

Article Mathematics, Applied

Stieltjes polynomials and Gauss-Kronrod quadrature for Jacobi weight functions

F Peherstorfer et al.

NUMERISCHE MATHEMATIK (2003)

Article Computer Science, Software Engineering

Symmetric Gauss-Lobatto and modified anti-Gauss rules

D Calvetti et al.

BIT NUMERICAL MATHEMATICS (2003)

Article Mathematics, Applied

On stratified extensions of Gauss-Laguerre and Gauss-Hermite quadrature formulas

S Ehrich

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2002)

Article Mathematics, Applied

Computation of Gauss-type quadrature formulas

DP Laurie

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2001)

Article Mathematics, Applied

Computation of Gauss-Kronrod quadrature rules

D Calvetti et al.

MATHEMATICS OF COMPUTATION (2000)

Article Mathematics, Applied

Ultraspherical Gauss-Kronrod quadrature is not possible for λ > 3

F Peherstorfer et al.

SIAM JOURNAL ON NUMERICAL ANALYSIS (2000)