An algorithm for approximating the singular triplets of complex symmetric matrices

✍ Scribed by V. Simoncini; E. Sjöström

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 172 KB
• Volume: 4
• Category: Article
• ISSN: 1070-5325
• DOI: 10.1002/(sici)1099-1506(199711/12)4:6<469::aid-nla122>3.0.co;2-a

✦ Synopsis

We present an algorithm for the approximation of the dominant singular values and corresponding right and left singular vectors of a complex symmetric matrix. The method is based on two short-term recurrences first proposed by Saunders, Simon and Yip for a non-Hermitian linear system solver. With symmetric matrices, the recurrence can be modified so as to generate a tridiagonal symmetric matrix from which the original triplets can be approximated. The recurrence formally resembles the Lanczos method, in spite of substantial differences which make usual convergence results inapplicable. Implementation aspects are discussed, such as re-orthogonalization and the use of alternative representation matrices. The method is very efficient over existing approaches which do not exploit the symmetry of the problem. Numerical experiments on application problems validate the analysis, while showing satisfactory results, especially on dense matrices.