Verified Computation of Square Roots of a Matrix

DOI10.1137/090757058zbMath1194.65069OpenAlexW2072944785MaRDI QIDQ3584160

Behnam Hashemi, Andreas Frommer

Publication date: 19 August 2010

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

Full work available at URL: https://doi.org/10.1137/090757058

zbMATH Keywords

circular arithmeticinterval analysismatrix square rootBrouwer's fixed point theoremKrawczyk's methodKronecker structures

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Interval and finite arithmetic (65G30) Algorithms with automatic result verification (65G20) Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items (15)

Computing enclosures for the matrix Mittag-Leffler function ⋮ The weighted Moore-Penrose generalized inverse and the force analysis of overconstrained parallel mechanisms ⋮ Methods for verified stabilizing solutions to continuous-time algebraic Riccati equations ⋮ Verified computation of matrix gamma function ⋮ Verified computation of real powers of matrices ⋮ Fast enclosing the solution set of the parametric Sylvester matrix equations ⋮ Fast verified computation for the matrix principal \(p\)th root ⋮ The interval Lyapunov matrix equation: analytical results and an efficient numerical technique for outer estimation of the united solution set ⋮ Efficient approaches for enclosing the united solution set of the interval generalized Sylvester matrix equations ⋮ Fast verified computation for real powers of large matrices with Kronecker structure ⋮ Verified error bounds for solutions of Sylvester matrix equations ⋮ The united stable solution set of interval continuous-time algebraic Riccati equation and veri ed numerical computation of its outer estimation ⋮ Computing enclosures for the inverse square root and the sign function of a matrix ⋮ Verified computation for the geometric mean of two matrices ⋮ An improved verification algorithm for nonlinear systems of equations based on Krawczyk operator

Uses Software

• C-XSC 2.0
• INTLAB
• INTOPT_90
• mctoolbox

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