Fast verified computation for the matrix principal \(p\)th root

DOI10.1016/j.cam.2017.08.018zbMath1376.65077OpenAlexW2752266465MaRDI QIDQ1675959

Shinya Miyajima

Publication date: 3 November 2017

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2017.08.018

zbMATH Keywords

algorithmnumerical resultsspectral decompositioncomputational efficiencyinterval matrixmatrix \(p\)th rootverified computationprincipal \(p\)th root

Mathematics Subject Classification ID

Interval and finite arithmetic (65G30) Complexity and performance of numerical algorithms (65Y20) Algorithms with automatic result verification (65G20) Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items (8)

Computing enclosures for the matrix Mittag-Leffler function ⋮ Verified computation of matrix gamma function ⋮ Verified computation of real powers of matrices ⋮ Verified computation for the matrix principal logarithm ⋮ Fast verified computation for real powers of large matrices with Kronecker structure ⋮ Fast verified computation for the minimal nonnegative solution of the nonsymmetric algebraic Riccati equation ⋮ Verified computation for the geometric mean of two matrices ⋮ Verified computation for the matrix Lambert \(W\) function

Uses Software

• INTLAB
• mctoolbox
• mftoolbox

Cites Work

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• Verification methods: Rigorous results using floating-point arithmetic
• Fast Enclosure for All Eigenvalues and Invariant Subspaces in Generalized Eigenvalue Problems
• An Algorithm for Computing Reducing Subspaces by Block Diagonalization
• On the Newton Method for the Matrix Pth Root
• Verified Computation of Square Roots of a Matrix
• A Family of Rational Iterations and Its Application to the Computation of the Matrix pth Root
• A Schur Algorithm for Computing Matrix pth Roots
• A Schur–Newton Method for the Matrix \lowercase{\boldmathp}th Root and its Inverse
• Energy-preserving $H^1$-Galerkin schemes for the Hunter--Saxton equation
• Functions of Matrices

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