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A Numerical Algorithm for Block-Diagonal Decomposition of Matrix *-Algebras, Part II: General Algorithm

Takanori Maehara(maehara***at***misojiro.t.u-tokyo.ac.jp)
Kazuo Murota(murota***at***mist.i.u-tokyo.ac.jp)

Abstract: An algorithm is proposed for finding the finest simultaneous block-diagonalization of a finite number of square matrices, or equivalently the irreducible decomposition of a matrix *-algebra given in terms of its generators. This extends the approach initiated in Part I by Murota-Kanno-Kojima-Kojima. The algorithm, composed of numerical-linear algebraic computations, does not require any algebraic structure to be known in advance. The main ingredient of the algorithm is the Schur decomposition and its skew-Hamiltonian variant for eigenvalue computation.

Keywords: matrix *-algebra, block-diagonalization, group symmetry, Schur decomposition, skew-Hamiltonian Schur decomposition

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 2: Applications -- Science and Engineering

Citation: METR 2008-26, Department of Mathematical Informatics, University of Tokyo, Japan, May 2008 (revised in May 2009).

Download: [PDF]

Entry Submitted: 05/11/2009
Entry Accepted: 05/11/2009
Entry Last Modified: 05/11/2009

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