Taro Konda

A new algorithm for singular value decomposition and its parallelization

An algorithm mainly consisting of a part of Divide and Conquer and the twisted factorization is proposed for bidiagonal SVD. The algorithm costs O(n^2)flops and is highly parallelizable when singular values are isolated. If strong clusters exist, the singular vector computation needs reorthgonalization. In such case, the cost of the algorithm increases to O(n^2+nk^2)flops and the parallelism may worsen depending on the distribution of singular values. Here k is the size of the largest cluster. The algorithm needs only O(n) working memory for every type of matrices.

An Evaluation of Double Divide and Conquer on a Multi-core

For bidiagonal SVD, double Divide and Conquer was proposed. It first computes singular values by a compact version of Divide and Conquer. The corresponding singular vectors are then computed by twisted factorization. The speed and accuracy of double Divide and Conquer are as good or even better than standard algorithms such as QR and the original Divide and Conquer. Moreover, it shows high scalability even on a PC cluster, distributed memory architecture. This paper presents an evaluation of parallel double Divide and Conquer for singular value decomposition on a multi-core architecture.