Name
Abstract | ||
|---|---|---|
The study of quaternion matrices has gained interest in many areas in recent years, and the problem of diagonalizing such matrices has also attracted attention. In this article, we present an algorithm for computing the SVD of a matrix with quaternion coefficients directly in quaternion arithmetic using a generalization of classical complex Jacobi methods. The extension of the Jacobi transformation to the quaternion case is introduced for the diagonalization of a Hermitian quaternion valued matrix. Based on this, an implicit Jacobi algorithm is proposed for computing the SVD of a quaternion matrix. The performance of the proposed algorithm is presented and compared with an already known algorithm using a complex equivalent of the quaternion matrix, and shown to be superior in execution time and accuracy. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1016/j.amc.2006.09.055 | Applied Mathematics and Computation |
Keywords | Field | DocType |
quaternion case,quaternion jacobi rotation,quaternion matrix singular value,complex equivalent,implicit jacobi algorithm,quaternion coefficient,hermitian quaternion,proposed algorithm,svd of a quaternion matrix,classical complex jacobi method,implicit svd algorithm,quaternion arithmetic,jacobi transformation,quaternion matrix,jacobi method,singular value decomposition | Singular value decomposition,Jacobi method,Algebra,Matrix (mathematics),Quaternion,Jacobi eigenvalue algorithm,Quaternion algebra,Hermitian matrix,Hypercomplex analysis,Mathematics | Journal |
Volume | Issue | ISSN |
187 | 2 | Applied Mathematics and Computation |
Citations | PageRank | References |
17 | 1.07 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Nicolas Le Bihan | 1 | 254 | 23.35 |
| Stephen J. Sangwine | 2 | 130 | 19.63 |