| 双变量LMEs一种异类约束最小二乘解的MCG算法 |
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| 引用本文： | 刘晓敏,张凯院.双变量LMEs一种异类约束最小二乘解的MCG算法[J].应用数学学报,2011,34(5). |
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| 作者姓名： | 刘晓敏 张凯院 |
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| 作者单位： | 西北工业大学应用数学系,西安,710072 |
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| 基金项目： | 国家自然科学基金(11071196)资助项目 |
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| 摘 要： | 借鉴求线性矩阵方程组(LMEs)同类约束最小二乘解的修正共轭梯度法,建立了求双变量LMEs的一种异类约束最小二乘解的修正共轭梯度法,并证明了该算法的收敛性.在不考虑舍入误差的情况下,利用该算法不仅可在有限步计算后得到LMEs的一组异类约束最小二乘解,而且选取特殊初始矩阵时,可求得LMEs的极小范数异类约束最小二乘解.另外,还可求得指定矩阵在该LMEs的异类约束最小二乘解集合中的最佳逼近.算例表明,该算法是有效的.
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| 关 键 词： | 线性矩阵方程组 异类约束最小二乘解 修正共轭梯度法 最佳逼近 |
MCG Method for a Different Constrained Least Square Solution of Two-variables Linear Matrix Equations for Recurrent Event Data |
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| LIU XIAOMIN
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ZHANG KAIYUAN.MCG Method for a Different Constrained Least Square Solution of Two-variables Linear Matrix Equations for Recurrent Event Data[J].Acta Mathematicae Applicatae Sinica,2011,34(5). |
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| Authors: | LIU XIAOMIN ZHANG KAIYUAN |
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| Affiliation: | LIU XIAOMIN,ZHANG KAIYUAN (Department of Applied Mathematics,Northwestern Polytechnical University,Xi'an 710072) |
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| Abstract: | Based on the modified conjugate gradient method for same constrained least square solution of the linear matrix equations,a modified conjugate gradient method is constructed for different constrained least square solution of the linear matrix equations with two variables.And the convergence of this method can be proved.By this method, a different constrained least square solution can be obtained within finite iterative steps in absence of roundoff errors,and the different constrained least square solution w... |
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| Keywords: | linear matrix equations different constrained least square solution modified conjugate gradient method optimal approximation |
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