Numerical approximation of the product of the square root of a matrix with a vector

DOI10.1016/S0024-3795(00)00068-9zbMath0972.65029WikidataQ126819159 ScholiaQ126819159MaRDI QIDQ1978127

S. K. Boyd, James Baglama, Edward J. Allen

Publication date: 11 November 2001

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

zbMATH Keywords

convergenceNewton's methodLanczos methoditerative methodinitial value problemmatrix square rootHilbert matrixRunge-Kutta-Fehlberg methodKrylov subspace procedure

Mathematics Subject Classification ID

Related Items (17)

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Cites Work

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• Computing real square roots of a real matrix
• A Schur method for the square root of a matrix
• A fast method for computing the principal \(n\)-th roots of complex matrices
• Roots of real matrices
• A faster, more stable method for comuting the pth roots of positive definite matrices
• Stable iterations for the matrix square root
• A power method for computing square roots of complex matrices
• Matrix Analysis
• On the Matrix Square Root
• A Padé Approximation Method for Square Roots of Symmetric Positive Definite Matrices
• On Krylov Subspace Approximations to the Matrix Exponential Operator
• Extended Krylov Subspaces: Approximation of the Matrix Square Root and Related Functions
• Newton's Method for the Matrix Square Root

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