| 等式约束不定最小二乘问题的双曲MGS消去算法 |
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| 引用本文： | 石崇,刘巧华.等式约束不定最小二乘问题的双曲MGS消去算法[J].应用数学与计算数学学报,2011,25(1):65-73. |
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| 作者姓名： | 石崇 刘巧华 |
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| 作者单位： | 上海大学理学院,上海,200444 |
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| 基金项目： | Project supported by the Natural Science Foundation of China(11001167); Shanghai Leading Academic Discipline Project(J50101) |
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| 摘 要： | 众所周知,加权法是解等式约束不定最小二乘问题的方法之一.通过探讨极限意义下,双曲MGS算法解对应加权问题的本质,得到一类消去算法.实验表明,该算法以和文献中现有的GHQR算法达到一样的精度,但实际计算量只需要GHQR算法的一半.
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| 关 键 词： | 等式约束不定最小二乘问题 双曲QR分解 双曲MGS算法 双曲MGS消去算法 |
A hyperbolic MGS elimination method for solving the equality constrained indefinite least squares problem |
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| SHI Chong,LIU Qiao-hua.A hyperbolic MGS elimination method for solving the equality constrained indefinite least squares problem[J].Communication on Applied Mathematics and Computation,2011,25(1):65-73. |
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| Authors: | SHI Chong LIU Qiao-hua |
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| Affiliation: | SHI Chong,LIU Qiao-hua (College of Sciences,Shanghai University,Shanghai 200444,China) |
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| Abstract: | It is well known that the method of weighting is an alternative method to solve the equality constrained indefinite least squares（ILSE） problem.Based on this observation,a type of elimination method is given by applying the hyperbolic modified Gram-Schmidt to the equivalent weighted problem and taking the limit analytically.Numerical experiments show that the method obtained can be as accurate as the GHQR method of Bojanczyk,et al.,but requires half operations of the GHQR method. |
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| Keywords: | equality constrained indefinite least squares problem hyperbolic QR factorization hyperbolic modified Gram-Schmidt elimination method |
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