Limited Memory Block Krylov Subspace Optimization
LMSVD is a MATLAB solver for computing dominant singular value decompositions of large and dense or unstructured matrices. The approach is based on a block Krylov subspace optimization technique which significantly accelerates the classic simultaneous iteration method.
Consider a real matrix ( without loss of generality) and a given positive integer . The task is to find two orthogonal matrices and , and a diagonal matrix whose diagonal entries are the largest singular values of , say, , such that
The approximation is called the -th dominant singular value decomposition of .
Xin Liu, Zaiwen Wen and Yin Zhang, Limited Memory Block Krylov Subspace Optimization for Computing Dominant Singular Value Decompositions, submitted. Rice CAAM Tech Report. (pdf)
LMSVD is distributed under the terms of the GNU General Public License.
>> addpath <lmsvd-root>