## Dept. of Mathematics and Computer Science (Berlin)

Your review has been received.

**Thank you very much.**

**reviewer:** Miloslav Znojil
**reviewernum:** 9689

**revieweremail:** znojil@ujf.cas.cz

**zblno:** DE015198231

**author:** Simon, Horst D.; Zha, Hongyuan:

**shorttitle:** Low-rank matrix approximation using the Lanczos bidiagonalization

**source:** SIAM J. Sci. Comput. 21, No. 6, 2257 - 2274 (2000)

**rpclass:** 68P30

**rsclass:** 15A12; 65F10; 62P99; 62D05; 62-07; 62B05

**keywords:** low-rank approximation of matrices,

**revtext:**
Approximations B (of rank j) of a given large non-square matrix A
are studied. Their optimal form is defined as a minimizer of the
Frobenius norm of the difference A - B. In principle, it can be
constructed via a j-dimensional part (projection) of a certain
diagonalized form of A. In such a setting one would need the full
singular value decomposition of A (which generalizes the current
diagonalization using two orthogonal matrices P and Q).
The paper offers a cheaper algorithm based on the Lanczos
bidiagonalization. The authors perform the error and stopping
analysis and demonstrate that a mere one-sided
re-orthogonalization of this process guarantees a sufficient
precision. A collection of matrices from several application areas
is used in illustrative tests.

review-form Generator ()

Written by
*
Michael Jost* (jo@zblmath.FIZ-Karlsruhe.DE).