An algorithm to compute the square root of a 3\(\times 3\) positive definite matrix

DOI10.1016/0898-1221(89)90240-XzbMath0686.65019OpenAlexW2061589544MaRDI QIDQ1262698

Leopoldo P. Franca

Publication date: 1989

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0898-1221(89)90240-x

zbMATH Keywords

eigenvalueCayley-Hamilton theoremstrain tensorstretch tensorsquare root of a positive definite matrix

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items

The weighted Moore-Penrose generalized inverse and the force analysis of overconstrained parallel mechanisms, A robust algorithm for finding the eigenvalues and eigenvectors of \(3 \times 3\) symmetric matrices, On the determination of deformation from strain, A Splitting Scheme for Flip-Free Distortion Energies, Non-associative \(J_2\) plasticity model for finite element buckling analysis of shells in the inelastic range, \(\mathbf{U} = \mathbf{C}^{1/2}\) and its invariants in terms of \(\mathbf{C}\) and its invariants, \texttt{bimEX}: a Mathematica package for exact computations in \(3 + 1\) bimetric relativity, The Galerkin gradient least-squares method, Shape-aware matching of implicit surfaces based on thin shell energies, Newton's method for the matrix nonsingular square root

Cites Work

• Determination of \(C^{1/2}\), \(C^{-1/2}\) and more general isotropic tensor functions of C
• Determination of the stretch and rotation in the polar decomposition of the deformation gradient
• Unnamed Item
• Unnamed Item