Generalized averaged Gauss quadrature rules for the approximation of matrix functionals

DOI10.1007/s10543-015-0592-7zbMath1352.65089OpenAlexW2278113833MaRDI QIDQ329025

Tunan Tang, Miodrag M. Spalević, Lothar Reichel

Publication date: 21 October 2016

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-015-0592-7

zbMATH Keywords

numerical exampleGauss quadraturegeneralized averaged Gauss quadrature rulehigher accuracymatrix functionalnon-Hermitian Lanczos process

Mathematics Subject Classification ID

Algorithms for approximation of functions (65D15) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items (18)

Averaged Gauss quadrature formulas: properties and applications ⋮ Matrix functions in network analysis ⋮ Decompositions of optimal averaged Gauss quadrature rules ⋮ Averaged cubature schemes on the real positive semiaxis ⋮ Modified Stieltjes polynomials and Gauss-Kronrod quadrature rules ⋮ Optimal averaged Padé-type approximants ⋮ On generalized averaged Gaussian formulas. II ⋮ A note on generalized averaged Gaussian formulas for a class of weight functions ⋮ Estimating the error in matrix function approximations ⋮ Unnamed Item ⋮ A Structure Preserving Lanczos Algorithm for Computing the Optical Absorption Spectrum ⋮ Enhanced matrix function approximation ⋮ A new representation of generalized averaged Gauss quadrature rules ⋮ Internality of generalized averaged Gaussian quadrature rules and truncated variants for modified Chebyshev measures of the second kind ⋮ Generalized averaged Szegő quadrature rules ⋮ Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the first kind ⋮ Truncated generalized averaged Gauss quadrature rules ⋮ Internality of generalized averaged Gaussian quadrature rules and truncated variants for measures induced by Chebyshev polynomials

Uses Software

• Pajek
• Pajek datasets
• OPQ
• mftoolbox
• sgcen
• blgaussexp

Cites Work

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• Some large-scale matrix computation problems
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• Network Properties Revealed through Matrix Functions
• On generalized averaged Gaussian formulas
• On Generating Orthogonal Polynomials
• Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator
• A Breakdown-Free Variation of the Nonsymmetric Lanczos Algorithms
• Calculation of Gauss-Kronrod quadrature rules
• Computation of Gauss-Kronrod quadrature rules
• Block Gauss and Anti-Gauss Quadrature with Application to Networks
• Functions of Matrices
• Calculation of Gauss Quadrature Rules
• An overview of the computational aspects of Kronrod quadrature rules
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