Fast approximate truncated SVD

Abstract

Summary This paper presents a new method for the computation of truncated singular value decomposition (SVD) of an arbitrary matrix. The method can be qualified as deterministic because it does not use randomized schemes. The number of operations required is asymptotically lower than that using conventional methods for nonsymmetric matrices and is at a par with the best existing deterministic methods for unstructured symmetric ones. It slightly exceeds the asymptotical computational cost of SVD methods based on randomization; however, the error estimate for such methods is significantly higher than for the presented one. The method is one‐pass, that is, each value of the matrix is used just once. It is also readily parallelizable. In the case of full SVD decomposition, it is exact. In addition, it can be modified for a case when data are obtained sequentially rather than being available all at once. Numerical simulations confirm accuracy of the method.