Computation of the matrix \(p\)th root and its Fréchet derivative by integrals

zbMath1287.65035MaRDI QIDQ2447393

João R. Cardoso

Publication date: 25 April 2014

Published in: ETNA. Electronic Transactions on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://www.emis.de/journals/ETNA/vol.39.2012/pp414-436.dir/pp414-436.html

zbMATH Keywords

Fréchet derivativequadraturematrix \(p\)th rootcomposite trapezoidal ruleGauss-Legendre ruleadaptive Simpson rule

Mathematics Subject Classification ID

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

Related Items (8)

Iterative Computation of the Fréchet Derivative of the Polar Decomposition ⋮ Computing the Weighted Geometric Mean of Two Large-Scale Matrices and Its Inverse Times a Vector ⋮ Algorithms for the computation of the matrix logarithm based on the double exponential formula ⋮ Generalized product of two square matrices and application for some algebraic equations ⋮ The complex step approximation to the higher order Fréchet derivatives of a matrix function ⋮ Estimation of dynamic discrete models from time aggregated data ⋮ Computing the matrix fractional power with the double exponential formula ⋮ Integral representations for higher-order Fréchet derivatives of matrix functions: quadrature algorithms and new results on the level-2 condition number

Uses Software

• Mulprec
• Algorithm 432

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