Controllability properties of the inverse power method on projective space are investigated. For complex eigenvalue shifts a simple characterization of the reachable sets in terms of invariant subspaces can be obtained. The real case is more complicated and is investigated in this paper. Necessary and suucient conditions for complete controllability are obtained in terms of the solvability of a...

In the case of a source-free plane-layered elastic medium, and for direct rays, the formal series ‘solution’ of the elastic equations in inverse powers of frequency can be obtained to any desired order by a process of integration by parts of a suitable iterate. The second iteration of the standard wave vector must be employed to ensure that all O(w-‘) terms are included in the iterative solutio...

Suppose that one knows an accurate approximation to an eigenvalue of a real symmetric tridiagonal matrix. A variant of deflation by the Givens rotations is proposed in order to split off the approximated eigenvalue. Such a deflation can be used instead of inverse iteration to compute the corresponding eigenvector. © 2002 Elsevier Science Inc. All rights reserved.

in this paper, a numerical method for nding minimal solution of a mn fullyfuzzy linear system of the form ax = b based on pseudo inverse calculation,is given when the central matrix of coecients is row full rank or column fullrank, and where a~ is a non-negative fuzzy mn matrix, the unknown vectorx is a vector consisting of n non-negative fuzzy numbers and the constant b isa vector consisti...

An iterative method is introduced for solving noisy, ill-conditioned inverse problems. Analysis of the semi-convergence behavior identifies three error components iteration error, noise error, and initial guess error. A derived expression explains how the three errors are related to each other relative to the number of iterations. The Standard Tikhonov regularization method is just the first it...

The preconditioned inverse iteration [Ney01a] is an efficient method to compute the smallest eigenpair of a symmetric positive definite matrix M . Here we use this method to find the smallest eigenvalues of a hierarchical matrix [Hac99]. The storage complexity of the datasparse H-matrices is almost linear. We use H-arithmetic to precondition with an approximate inverse of M or an approximate Ch...

As part of the Fujitsu-ANU Parallel Mathematical Subroutine Library Project we have developed a suite of parallel eigenvalue decomposition routines to handle a variety of input matrices. For a dense real symmetric matrix there are routines using the Jacobi algorithm and routines which rst reduce the symmetric matrix to tridiagonal form. All algorithms have been developed to fully exploit the ve...

Newton’s iteration is modified for the computation of the group inverses of singular Toeplitz matrices. At each iteration, the iteration matrix is approximated by a matrix with a low displacement rank. Because of the displacement structure of the iteration matrix, the matrix-vector multiplication involved in Newton’s iteration can be done efficiently. We show that the convergence of the modifie...

We present a method to solve the inverse problem in pulsed photothermal radiometry sPPTRd that exploits advantages of truncated singular value decomposition sT-SVDd while imposing a non-negativity constraint to the solution. The presented method is a hybrid in the sense that it expresses the solution vector as a linear superposition of right singular vectors, but with a non-negative constraint ...

We propose and study the iteration-complexity of an inexact version of the Spingarn’s partial inverse method. Its complexity analysis is performed by viewing it in the framework of the hybrid proximal extragradient (HPE) method, for which pointwise and ergodic iteration-complexity has been established recently by Monteiro and Svaiter. As applications, we propose and analyze the iteration-comple...