A Schur Algorithm for Computing Matrix pth Roots

DOI10.1137/S0895479801392697zbMath1040.65038MaRDI QIDQ4443784

Matthew I. Smith

Publication date: 18 January 2004

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

zbMATH Keywords

stabilityNewton's methodSchur algorithmcommutativitymatrix \(p\)th rootrounding error analysisreal arithmetic

Mathematics Subject Classification ID

Related Items (34)

Nonlinear matrix equations and structured linear algebra ⋮ Matrix roots of imprimitive irreducible nonnegative matrices ⋮ Computing the Square Root of a Low-Rank Perturbation of the Scaled Identity Matrix ⋮ On explicit formulas of the principal matrix \(p\)th root by polynomial decompositions ⋮ Computing primary solutions of equations involving primary matrix functions ⋮ A technique for improving the computation of functions of triangular matrices ⋮ On Newton's method and Halley's method for the principal \(p\)th root of a matrix ⋮ 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 square roots of matrices with central symmetry ⋮ Fast verified computation for the matrix principal \(p\)th root ⋮ New Hermite series expansion for computing the matrix hyperbolic cosine ⋮ Approximation of the \(p\)th roots of a matrix by using trapezoid rule ⋮ Some new characterizations of a Hermitian matrix and their applications ⋮ Substitution algorithms for rational matrix equations ⋮ \(m\) th roots of \(H\)-selfadjoint matrices ⋮ On stochasticity preserving methods for the computation of the matrix \(p\)th root ⋮ Least-squares collocation with covariance-matching constraints ⋮ A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices ⋮ Matrix roots of eventually positive matrices ⋮ A numerical study of fractional linear algebraic systems ⋮ The dual Padé families of iterations for the matrix \(p\)th root and the matrix \(p\)-sector function ⋮ On \(p\)th roots of stochastic matrices ⋮ Residual methods for the large-scale matrix \(p\)th root and some related problems ⋮ Algorithms for the matrix \(p\)th root ⋮ Unnamed Item ⋮ A binary powering Schur algorithm for computing primary matrix roots ⋮ A study of Schröder's method for the matrix \(p\)th root using power series expansions ⋮ Local Identification of Piecewise Deterministic Models of Genetic Networks ⋮ Rational minimax iterations for computing the matrix \(p\)th root ⋮ Testing Matrix Function Algorithms Using Identities ⋮ Unnamed Item ⋮ Explicit convergence regions of Newton's method and Chebyshev's method for the matrix \(p\)th root ⋮ Generalized fractional algebraic linear system solvers

Uses Software

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