On Newton's method and Halley's method for the principal \(p\)th root of a matrix

DOI10.1016/j.laa.2009.02.030zbMath1190.65065OpenAlexW2117547260MaRDI QIDQ848572

Chun-Hua Guo

Publication date: 4 March 2010

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2009.02.030

zbMATH Keywords

convergenceNewton's methodnumerical examplesseries expansion\(M\)-matrixHalley's method\(H\)-matrixmatrix \(p\)th root

Mathematics Subject Classification ID

Matrix equations and identities (15A24)

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Uses Software

• mctoolbox
• mftoolbox

Cites Work

• Computing real square roots of a real matrix
• A Schur method for the square root of a matrix
• Inverse M-matrices
• Algorithms for the matrix \(p\)th root
• Analytic functions ofM-matrices and generalizations
• On the Newton Method for the Matrix Pth Root
• A Family of Rational Iterations and Its Application to the Computation of the Matrix pth Root
• On the Computation of the Matrixk-th Root
• Inequalities for M-matrices
• A Schur Algorithm for Computing Matrix pth Roots
• The Matrix Square Root from a New Functional Perspective: Theoretical Results and Computational Issues
• A Schur–Newton Method for the Matrix \lowercase{\boldmathp}th Root and its Inverse
• Functions of Matrices
• Iterative Solution of a Nonsymmetric Algebraic Riccati Equation
• Infinite product expansions for matrix n-th roots
• On the square root of an H-matrix with positive diagonal elements