A Schur Logarithmic Algorithm for Fractional Powers of Matrices

DOI10.1137/120877398zbMath1273.65061OpenAlexW2060933228MaRDI QIDQ2848638

Carlo Manasse, Bruno Iannazzo

Publication date: 26 September 2013

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/f4b268211481f68d3529c843de0bb1b6bbc5f0a0

zbMATH Keywords

binary powering techniquematrix \(p\)th rootprimary matrix functionfractional power of a matrixSchur recurrence method

Mathematics Subject Classification ID

Related Items (14)

Computing the Square Root of a Low-Rank Perturbation of the Scaled Identity Matrix ⋮ Computing primary solutions of equations involving primary matrix functions ⋮ A technique for improving the computation of functions of triangular matrices ⋮ On a new family of high‐order iterative methods for the matrix pth root ⋮ Monotonicity and positivity of coefficients of power series expansions associated with Newton and Halley methods for the matrix \(p\)th root ⋮ Computing the Weighted Geometric Mean of Two Large-Scale Matrices and Its Inverse Times a Vector ⋮ Substitution algorithms for rational matrix equations ⋮ Rational Krylov methods for functions of matrices with applications to fractional partial differential equations ⋮ The dual Padé families of iterations for the matrix \(p\)th root and the matrix \(p\)-sector function ⋮ The geometric mean of two matrices from a computational viewpoint ⋮ A study of Schröder's method for the matrix \(p\)th root using power series expansions ⋮ Computing the matrix fractional power with the double exponential formula ⋮ Testing Matrix Function Algorithms Using Identities ⋮ Explicit convergence regions of Newton's method and Chebyshev's method for the matrix \(p\)th root

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