The purpose of this paper is to derive the generalized conjugate residual(GCR)algorithm for finding the least squares solution on a class of Sylvester matrix equations.We prove that if the system is inconsistent,the l...The purpose of this paper is to derive the generalized conjugate residual(GCR)algorithm for finding the least squares solution on a class of Sylvester matrix equations.We prove that if the system is inconsistent,the least squares solution can be obtained within finite iterative steps in the absence of round-off errors.Furthermore,we provide a method for choosing the initial matrix to obtain the minimum norm least squares solution of the problem.Finally,we give some numerical examples to illustrate the performance of GCR algorithm.展开更多
基金Supported by Fujian Natural ScienceFoundation(Grant No.2016J01005)Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB18010202).
文摘The purpose of this paper is to derive the generalized conjugate residual(GCR)algorithm for finding the least squares solution on a class of Sylvester matrix equations.We prove that if the system is inconsistent,the least squares solution can be obtained within finite iterative steps in the absence of round-off errors.Furthermore,we provide a method for choosing the initial matrix to obtain the minimum norm least squares solution of the problem.Finally,we give some numerical examples to illustrate the performance of GCR algorithm.
