In this article, we consider the structured condition numbers for LDU, factorization by using the modified matrix-vector approach and the differential calculus, which can be represented by sets of parameters. By setti...In this article, we consider the structured condition numbers for LDU, factorization by using the modified matrix-vector approach and the differential calculus, which can be represented by sets of parameters. By setting the specific norms and weight parameters, we present the expressions of the structured normwise, mixed, componentwise condition numbers and the corresponding results for unstructured ones. In addition, we investigate the statistical estimation of condition numbers of LDU factorization using the probabilistic spectral norm estimator and the small-sample statistical condition estimation method, and devise three algorithms. Finally, we compare the structured condition numbers with the corresponding unstructured ones in numerical experiments.展开更多
In this paper,we give the sensitivity analyses by two approaches for L,D,U in factorization A=LDU of general perturbations in A which sufficiently small in norm. By the matrix vector equation approach,we derive the sh...In this paper,we give the sensitivity analyses by two approaches for L,D,U in factorization A=LDU of general perturbations in A which sufficiently small in norm. By the matrix vector equation approach,we derive the sharp condition number for L,D and U factors .By the matrix equation approach we derive corresponding condition estimates. When A is a symmetric matrix,the corresponding results can be obtained for LDL T factorization.展开更多
基金Supported by the National Natural Science Foundation of China(11671060).
文摘In this article, we consider the structured condition numbers for LDU, factorization by using the modified matrix-vector approach and the differential calculus, which can be represented by sets of parameters. By setting the specific norms and weight parameters, we present the expressions of the structured normwise, mixed, componentwise condition numbers and the corresponding results for unstructured ones. In addition, we investigate the statistical estimation of condition numbers of LDU factorization using the probabilistic spectral norm estimator and the small-sample statistical condition estimation method, and devise three algorithms. Finally, we compare the structured condition numbers with the corresponding unstructured ones in numerical experiments.
基金863 project of China,under grantnumbers86 3-30 6 -ZD0 1 -0 3-2 ,86 3-30 6 -ZD1 1 -0 3-1,by 973project of Chinaundergrant number G1 9990 32 80 3
文摘In this paper,we give the sensitivity analyses by two approaches for L,D,U in factorization A=LDU of general perturbations in A which sufficiently small in norm. By the matrix vector equation approach,we derive the sharp condition number for L,D and U factors .By the matrix equation approach we derive corresponding condition estimates. When A is a symmetric matrix,the corresponding results can be obtained for LDL T factorization.
