Computation of matrix gamma function

DOI10.1007/s10543-018-00744-1OpenAlexW2810840768WikidataQ128641682 ScholiaQ128641682MaRDI QIDQ1999706

Amir Sadeghi, João R. Cardoso

Publication date: 27 June 2019

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.10554

zbMATH Keywords

Lanczos methodSchur decompositionStirling approximationreciprocal gamma functiongamma matrix functionblock Parlett recurrenceSpouge method

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items

A technique for improving the computation of functions of triangular matrices, The gamma function via interpolation, Verified computation of matrix gamma function, Calculating a function of a matrix with a real spectrum, Krylov Subspace Restarting for Matrix Laplace Transforms, On degenerate gamma matrix functions and related functions, AN ESTIMATE OF APPROXIMATION OF A MATRIX-VALUED FUNCTION BY AN INTERPOLATION POLYNOMIAL, Discrete matrix hypergeometric functions

Uses Software

• Algorithm 814
• mctoolbox
• mftoolbox

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Infinite matrix products and the representation of the matrix gamma function
• A recurrence among the elements of functions of triangular matrices
• On the hypergeometric matrix function
• Iterated exponentiation, matrix-matrix exponentiation, and entropy
• Asymptotics of the modified Bessel and the incomplete gamma matrix functions
• On the random gamma function: theory and computing
• Conditioning of the matrix-matrix exponentiation
• Talbot quadratures and rational approximations
• The special functions and their approximations. Vol. I, II
• Some properties of gamma and beta matrix functions
• Computing the Fréchet Derivative of the Matrix Logarithm and Estimating the Condition Number
• Approximation of Matrix-Valued Functions
• Improved Inverse Scaling and Squaring Algorithms for the Matrix Logarithm
• Leonhard Euler's Integral: A Historical Profile of the Gamma Function: In Memoriam: Milton Abramowitz
• Computing the Fréchet Derivative of the Matrix Exponential, with an Application to Condition Number Estimation
• Computing $A^\alpha, \log(A)$, and Related Matrix Functions by Contour Integrals
• On Stieltjes' Continued Fraction for the Gamma Function
• A Computational Procedure for Incomplete Gamma Functions
• The Sensitivity of the Matrix Exponential
• Computation of the Gamma, Digamma, and Trigamma Functions
• A Schur-Parlett Algorithm for Computing Matrix Functions
• A note on the recursive calculation of incomplete gamma functions
• Gamma and Factorial in the Monthly
• Computing the Gamma Function Using Contour Integrals and Rational Approximations
• Functions of Matrices
• Algorithm 814
• A Precision Approximation of the Gamma Function
• Concerning Two Series for the Gamma Function
• Calculation of the Gamma Function by Stirling's Formula
• On the Number of Nonscalar Multiplications Necessary to Evaluate Polynomials