Monotonicity and positivity of coefficients of power series expansions associated with Newton and Halley methods for the matrix \(p\)th root

DOI10.1016/j.laa.2018.07.006zbMath1416.65118OpenAlexW2868328658WikidataQ129550122 ScholiaQ129550122MaRDI QIDQ1668991

Di Lu, Chun-Hua Guo

Publication date: 29 August 2018

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

Full work available at URL: https://doi.org/10.1016/j.laa.2018.07.006

zbMATH Keywords

Newton's methodseries expansion\(M\)-matrixHalley's method\(H\)-matrixmatrix \(p\)th root

Mathematics Subject Classification ID

Related Items (2)

A study of Schröder's method for the matrix \(p\)th root using power series expansions ⋮ Explicit convergence regions of Newton's method and Chebyshev's method for the matrix \(p\)th root

Uses Software

• mftoolbox

Cites Work

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• Analytic functions ofM-matrices and generalizations
• A Schur–Padé Algorithm for Fractional Powers of a Matrix
• 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
• 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
• Partial Fraction Expansions for Newton's and Halley's Iterations for Square Roots
• Functions of Matrices
• A binary powering Schur algorithm for computing primary matrix roots

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