Dynamical methods for polar decomposition and inversion of matrices

DOI10.1016/S0024-3795(96)00235-2zbMath0879.15009OpenAlexW2055586001MaRDI QIDQ1359197

Neil H. Getz, Jerrold E. Marsden

Publication date: 22 January 1998

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

Full work available at URL: https://doi.org/10.1016/s0024-3795(96)00235-2

zbMATH Keywords

polar decompositionmatrix inversiondynamic inversiontime-varying matrix

Mathematics Subject Classification ID

Factorization of matrices (15A23) Theory of matrix inversion and generalized inverses (15A09) Inverse problems involving ordinary differential equations (34A55)

Related Items (6)

Geometry of matrix decompositions seen through optimal transport and information geometry ⋮ Exponential polar factorization of the fundamental matrix of linear differential systems ⋮ A 5-instant finite difference formula to find discrete time-varying generalized matrix inverses, matrix inverses, and scalar reciprocals ⋮ Discrete gradient-zeroing neural network algorithms for handling future quadratic program as well as robot arm via ten-instant formula ⋮ From Penrose equations to Zhang neural network, Getz-Marsden dynamic system, and DDD (direct derivative dynamics) using substitution technique ⋮ General 9-instant discrete-time Zhang neural network for time-dependent applications

Uses Software

• Algorithm 432

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dynamical systems that perform the singular value decomposition
• The QR algorithm and scattering for the finite nonperiodic Toda lattice
• Estimation, principal components and Hamiltonian systems
• Least squares matching problems
• Engineering applications of the Chow-Yorke algorithm
• Scaled Toda-like flows
• A recurrent neural network for real-time matrix inversion
• Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems
• Ein infinitesimales Analogon zum Quotienten-Differenzen-Algorithmus
• Matrix Analysis
• Robust nonlinear least squares estimation using the Chow-Yorke homotopy method
• A Hessenberg-Schur method for the problem AX + XB= C
• Matrix differential equations: a continuous realization process for linear algebra problems
• Dynamical Systems that Compute Balanced Realizations and the Singular Value Decomposition
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]

This page was built for publication: Dynamical methods for polar decomposition and inversion of matrices