Eigenvalue decomposition and singular value decomposition of matrices using Jacobi rotation
US7895254B2 · kind B2 · utility
Assignee
Inventors
Key dates
| Filing date | Nov 15, 2005 |
| Grant date | Feb 22, 2011 |
| Priority date | — |
| Expiry date | Mar 13, 2029 |
Classification
- Technology area (CPC H)Electricity
- CPC primaryH04L25/0248
- WIPO fieldDigital communication
- WIPO sectorElectrical engineering
Abstract
Techniques for decomposing matrices using Jacobi rotation are described. Multiple iterations of Jacobi rotation are performed on a first matrix of complex values with multiple Jacobi rotation matrices of complex values to zero out the off-diagonal elements in the first matrix. For each iteration, a submatrix may be formed based on the first matrix and decomposed to obtain eigenvectors for the submatrix, and a Jacobi rotation matrix may be formed with the eigenvectors and used to update the first matrix. A second matrix of complex values, which contains orthogonal vectors, is derived based on the Jacobi rotation matrices. For eigenvalue decomposition, a third matrix of eigenvalues may be derived based on the Jacobi rotation matrices. For singular value decomposition, a fourth matrix with left singular vectors and a matrix of singular values may be derived based on the Jacobi rotation matrices.
Source: USPTO / EPO open patent data. Objective bibliographic and citation counts.