Record number :

1553321

Title of article :

Eigenvalues for equivariant matrices

Author/Authors :

إhlander، نويسنده , , Krister and Munthe-Kaas، نويسنده , , Hans، نويسنده ,

Issue Information :

روزنامه با شماره پیاپی سال 2006

Pages :

11

From page :

89

To page :

99

Abstract :

An equivariant matrix A commutes with a group of permutation matrices. Such matrices often arise in numerical applications where the computational domain exhibits geometrical symmetries, for instance triangles, cubes, or icosahedra.
eory for block diagonalizing equivariant matrices via the generalized Fourier transform (GFT) is reviewed and applied to eigenvalue computations. For dense matrices which are equivariant under large symmetry groups, we give theoretical estimates that show a substantial performance gain. In case of cubic symmetry, the gain is about 800 times, which is verified by numerical results.
also shown how the multiplicity of the eigenvalues is determined by the symmetry, which thereby restricts the number of distinct eigenvalues. The inverse GFT is used to compute the corresponding eigenvectors. It is emphasized that the inverse transform in this case is very fast, due to the sparseness of the eigenvectors in the transformed space.

Keywords :

Generalized Fourier transform , Eigenvalue computation , Symmetrical geometry

Journal title :

Journal of Computational and Applied Mathematics

Journal title :

Journal of Computational and Applied Mathematics

Serial Year :

2006

Link To Document :