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Section B

On an iterative method for solving the least squares problem of rank-deficient systems

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Pages 532-541 | Received 07 Sep 2013, Accepted 16 Feb 2014, Published online: 23 May 2014
 

Abstract

In this paper, we first show an iterative method for finding the least squares (LS) solution to the inconsistent system Ax=b, where A is an m×n matrix of rank r. The method is an iteration scheme for consistent system of linear equations M= which is an augmented system associated with Ax=b. It denotes that under some conditions, the sequence, 0, 1, 2, … , converges to the LS solution of the system Ax=b for every initial vector 0, where (ME)iEi−1+, for i=1, 2, … . In our numerical test, we propose to find E without using decomposition methods. The improved timings are shown with matrices of substantial size.

2013 AMS Subject Classification:

Acknowledgement

The research is supported by Scientific Computing Key Laboratory of Shanghai University and the National Natural Science Foundation of China under grant 11271084.

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