A numerical algorithm for block-diagonal decomposition of matrix -algebras with application to semidefinite programming

Kazuo Murota*, Yoshihiro Kanno, Masakazu Kojima, Sadayoshi Kojima

*この研究の対応する著者

研究成果: Article査読

48 被引用数 (Scopus)

抄録

Motivated by recent interest in group-symmetry in semidefinite programming, we propose a numerical method for finding a finest simultaneous block-diago- nalization of a finite number of matrices, or equivalently the irreducible decomposition of the generated matrix *-algebra. The method is composed of numerical-linear algebraic computations such as eigenvalue computation, and automatically makes full use of the underlying algebraic structure, which is often an outcome of physical or geometrical symmetry, sparsity, and structural or numerical degeneracy in the given matrices. The main issues of the proposed approach are presented in this paper under some assumptions, while the companion paper gives an algorithm with full generality. Numerical examples of truss and frame designs are also presented.

本文言語English
ページ(範囲)125-160
ページ数36
ジャーナルJapan Journal of Industrial and Applied Mathematics
27
1
DOI
出版ステータスPublished - 2010 6月 1
外部発表はい

ASJC Scopus subject areas

  • 工学(全般)
  • 応用数学

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