RANK DETECTION METHODS FOR SPARSE MATRICES

作     者：BARLOW, JL VEMULAPATI, UB 

作者机构：OAK RIDGE NATL LAB OAK RIDGE TN 37831 USA UNIV CENT FLORIDA DEPT COMP SCI ORLANDO FL 32816 USA 

出 版 物：《SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS》 (工业与应用数学会矩阵分析和应用杂志)

年 卷 期：1992年第13卷第4期

页      面：1279-1297页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：SPARSE MATRICES ORTHOGONAL FACTORIZATION CONDITION ESTIMATION NUMERICAL RANK 

摘      要：A method is proposed for estimating the numerical rank of a sparse matrix. The method uses orthogonal factorization along with a one-norm incremental condition estimator that is an adaptation of the LINPACK estimator. This approach allows the use of static storage allocation as is used in SPARSPAK-B, whereas there is no known way to implement column pivoting without dynamic storage allocation. It is shown here that this approach is probably more accurate than the method presently used by SPARSPAK-B. The method is implemented with an overhead of O(n(U) log n) operations, where n(U) is the number of nonzeros in the upper triangular factor of the matrix. In theory, it can be implemented in O(max{n(U), n log n}) operations, but this requires the use of a complicated data structure. It is shown how a variant of this strategy may be implemented on a message-passing architecture. A prototype implementation is done and tests show that the method is accurate and efficient. Ways in which the condition estimator and the rank detection method can be used are also discussed, along with the rank-revealing orthogonal factorizations of Foster [Linear Algebra Appl., 74 (1986), pp. 47-72] and Chan [Linear Algebra Appl., 88/89 (1987), pp. 67-82].