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Full-Text Articles in Physical Sciences and Mathematics
Computing Singular Values Of Large Matrices With An Inverse-Free Preconditioned Krylov Subspace Method, Qiao Liang, Qiang Ye
Computing Singular Values Of Large Matrices With An Inverse-Free Preconditioned Krylov Subspace Method, Qiao Liang, Qiang Ye
Mathematics Faculty Publications
We present an efficient algorithm for computing a few extreme singular values of a large sparse m×n matrix C. Our algorithm is based on reformulating the singular value problem as an eigenvalue problem for CTC. To address the clustering of the singular values, we develop an inverse-free preconditioned Krylov subspace method to accelerate convergence. We consider preconditioning that is based on robust incomplete factorizations, and we discuss various implementation issues. Extensive numerical tests are presented to demonstrate efficiency and robustness of the new algorithm.
On The Intersection Of Certain Maximal Subgroups Of A Finite Group, Adolfo Ballester-Bolinches, James C. Beidleman, Hermann Heineken, Matthew F. Ragland, Jack Schmidt
On The Intersection Of Certain Maximal Subgroups Of A Finite Group, Adolfo Ballester-Bolinches, James C. Beidleman, Hermann Heineken, Matthew F. Ragland, Jack Schmidt
Mathematics Faculty Publications
Let Δ(G) denote the intersection of all non-normal maximal subgroups of a group G. We introduce the class of T2-groups which are defined as the groups G for which G/Δ(G) is a T-group, that is, a group in which normality is a transitive relation. Several results concerning the class T2 are discussed. In particular, if G is a solvable group, then Sylow permutability is a transitive relation in G if and only if every subgroup H of G is a T2-group such that the nilpotent residual of H …