Computing the Polar Decomposition and the Matrix Sign Decomposition in Matrix Groups
Copyright policy )Computing the Polar Decomposition and the Matrix Sign Decomposition in Matrix Groups
The polar decomposition of \(A\) is \(A=UH\), where \(A\) has complex elements, \(U\) is unitary, \(H\) is Hermitian positive semi-definite. The authors identify a family of globally convergent rational iterations that preserve group structure. They show how the structure preservation leads to particularly convenient convergence tests in the case of polar decomposition. They identify various pros and cons in the structured iterations versus Newton comparison, including the slightly better empirically observed numerical stability of the Newton method, the convergence prediction possible with structured iterations.
- Eastern Michigan University United States
- University of Salford United Kingdom
matrix sign decomposition, pseudo-orthogonal matrix, Sesquilinear form, Adjoint, Direct numerical methods for linear systems and matrix inversion, Matrix iteration, Symplectic matrix, Newton iteration, Bilinear form, Complex orthogonal matrix, Perplectic matrix, Polar decomposition, convergence, sesquilinear form, Other matrix algorithms, Matrix sign decomposition, structure preservation, Automorphism group, Structure preservation, polar decomposition, Pseudo-orthogonal matrix, matrix iteration, complex orthogonal matrix, automorphism group, bilinear form, perplectic matrix, symplectic matrix
matrix sign decomposition, pseudo-orthogonal matrix, Sesquilinear form, Adjoint, Direct numerical methods for linear systems and matrix inversion, Matrix iteration, Symplectic matrix, Newton iteration, Bilinear form, Complex orthogonal matrix, Perplectic matrix, Polar decomposition, convergence, sesquilinear form, Other matrix algorithms, Matrix sign decomposition, structure preservation, Automorphism group, Structure preservation, polar decomposition, Pseudo-orthogonal matrix, matrix iteration, complex orthogonal matrix, automorphism group, bilinear form, perplectic matrix, symplectic matrix
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