A comparison between the complex symmetric based and classical computation of the singular value decomposition of normal matrices

作者：Ferranti Micol; Thanh Hieu Le; Vandebril Raf^*

来源：Numerical Algorithms, 2014, 67(1): 109-120.

DOI：10.1007/s11075-013-9777-9

• Singular value decomposition
• Symmetric singular value decomposition
• Takagi factorization
• Normal matrix

An algorithm for computing the singular value decomposition of normal matrices using intermediate complex symmetric matrices is proposed. This algorithm, as most eigenvalue and singular value algorithms, consists of two steps. It is based on combining the unitarily equivalence of normal matrices to complex symmetric tridiagonal form with the symmetric singular value decomposition of complex symmetric matrices. Numerical experiments are included comparing several algorithms, with respect to speed and accuracy, for computing the symmetric singular value decomposition (also known as the Takagi factorization). Next we compare the novel approach with the classical Golub-Kahan method for computing the singular value decomposition of normal matrices: it is faster, consumes less memory, but on the other hand the results are significantly less accurate.

• 出版日期2014-9