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An Iterative Method for Different Constrained Least Square Solution of a Multi-Variables Linear Matrix Equation

机译:多元线性矩阵方程的不同约束最小二乘解的迭代方法

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An iterative method is constructed to find the different constrained least square solution by constructing the equivalent linear matrix equations, and revising the drop direction of the conjugate gradient method and its related coefficient, and its convergence is proved. By this iterative method, the different constrained least square solution can be obtained within finite iterative steps in the absence of round off errors, and the different constrained least square solution with least-norm can be got by choosing special initial matrix. In addition, the optimal approximation matrix to any given matrix can be obtained in the set of the different constrained least square solutions. The numerical examples show that the iterative method is efficient.
机译:通过构造等效线性矩阵方程,并修改共轭梯度法的落差方向及其相关系数,构造了一种迭代方法来找到不同的约束最小二乘解,并证明了其收敛性。通过这种迭代方法,可以在不存在舍入误差的情况下,在有限的迭代步骤内获得不同的约束最小二乘解,并且可以通过选择特殊的初始矩阵来获得具有最小范数的约束最小二乘解。另外,可以在一组不同的约束最小二乘解中获得对任何给定矩阵的最佳逼近矩阵。数值算例表明,该迭代方法是有效的。

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