关键词: 奇异值分解, QR算法, 大型矩阵, 矩阵分割, 双向收缩

Abstract:

Aimed at the essential reason of the algorithm when it is used to process the singular non-convergence of the traditional QR （Quadrature Right-triangle） value decomposition （SVD） of some large-scale matrixes, a doubledirection shrink and multi-partition method is proposed. In this method, the line dislodgment algorithms of nonzero element from left to right and from down to up, which greatly influence the accuracy of SVD, are investigated, and a searching algorithm for the first and the last rows of the sub-matrix is put forward to realize the partition of the main matrix. Thus, a multi-partition and double-direction shrink QR algorithm for the SVD of large-scale matrix is implemented. An example is then presented to reveal the difference of convergence speed between the non-partition and the multi-partition QR algorithms. The results indicate that the proposed algorithm realizes a smooth iteration process with less iteration number and high convergence speed, overcomes the non-convergence of the traditional QR algorithm, and realizes the high-speed SVD computation of any large-scale matrix.

Key words: singular value decomposition, QR algorithm, large-scale matrix, matrix partition, double-direction shrink