## Computing singular values of large matrices with an inverse-free preconditioned Krylov subspace method

Qiao Liang and Qiang Ye

### Abstract

We present an efficient algorithm for computing a few extreme singular values of a large sparse $m\!\times\!n$ matrix $C$. Our algorithm is based on reformulating the singular value problem as an eigenvalue problem for $C^TC$. To address the clustering of the singular values, we develop an inverse-free preconditioned Krylov subspace method to accelerate convergence. We consider preconditioning that is based on robust incomplete factorizations, and we discuss various implementation issues. Extensive numerical tests are presented to demonstrate efficiency and robustness of the new algorithm.

Full Text (PDF) [310 KB]

### Key words

singular values, inverse-free preconditioned Krylov Subspace Method, preconditioning, incomplete QR factorization, robust incomplete factorization

65F15, 65F08

### Links to the cited ETNA articles

 [26] Vol. 7 (1998), pp. 104-123 Andrew V. Knyazev: Preconditioned eigensolvers - an oxymoron?

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