| A NUMERICALLY STABLE BLOCK MODIFIED GRAM-SCHMIDT ALGORITHM FOR SOLVING STIFF WEIGHTED LEAST SQUARES PROBLEMS |
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| 作者姓名： | Musheng Wei Qiaohua Liu |
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| 作者单位： | [1]Department of Mathematics, East China Normal University, Shanghai 200062, China [2]Department of Mathematics, Shanghai University, Shanghai 200444, China |
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| 基金项目： | This work is supported by NSFC under grant No. 10371044, and Science and Technology Commission of Shanghai Muaicipality grant No. 04JC14031. |
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| 摘 要： |
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| 关 键 词： | 最小二乘方 加权 数值稳定性 排列 |
| 修稿时间： | 2005-04-18 |
A NUMERICALLY STABLE BLOCK MODIFIED GRAM-SCHMIDT ALGORITHM FOR SOLVING STIFF WEIGHTED LEAST SQUARES PROBLEMS |
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| Musheng Wei Qiaohua Liu.A NUMERICALLY STABLE BLOCK MODIFIED GRAM-SCHMIDT ALGORITHM FOR SOLVING STIFF WEIGHTED LEAST SQUARES PROBLEMS[J].Journal of Computational Mathematics,2007,25(5):595-619. |
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| Abstract: | Recently, Wei in proved that perturbed stiff weighted pseudoinverses and stiff weighted least squares problems are stable, if and only if the original and perturbed coefficient matrices A and A^- satisfy several row rank preservation conditions. According to these conditions, in this paper we show that in general, ordinary modified Gram-Schmidt with column pivoting is not numerically stable for solving the stiff weighted least squares problem. We then propose a row block modified Gram-Schmidt algorithm with column pivoting, and show that with appropriately chosen tolerance, this algorithm can correctly determine the numerical ranks of these row partitioned sub-matrices, and the computed QR factor R^- contains small roundoff error which is row stable. Several numerical experiments are also provided to compare the results of the ordinary Modified Gram-Schmidt algorithm with column pivoting and the row block Modified Gram-Schmidt algorithm with column pivoting. |
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| Keywords: | Weighted least squares Stiff Row block MGS QR Numerical stability Rank preserve |
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