The standard incomplete LU (ILU) preconditioners often fail for general sparse in-deenite matrices because they give rise tòunstable' factors L and U. In such cases, it may be attractive to approximate the inverse of the matrix directly. This paper focuses on approximate inverse preconditioners based on minimizing kI ? AMk F , where AM is the preconditioned matrix. An iterative descent-type met...

By making use of duality mappings, we formulate an inexact Newton– Landweber iteration method for solving nonlinear inverse problems in Banach spaces. The method consists of two components: an outer Newton iteration and an inner scheme providing the increments by applying the Landweber iteration in Banach spaces to the local linearized equations. It has the advantage of reducing computational w...

In this paper, we propose a multi-level finite element method for the transmission eigenvalue problem of anisotropic media. The problem is non-standard and non-self-adjoint with important applications in inverse scattering theory. We employ a suitable finite element method to discretize the problem. The resulting generalized matrix eigenvalue problem is large, sparse and non-Hermitian. To compu...

The problem of reconstructing an unknown electric conductivity from boundary measurements has applications in medical imaging, geophysics, and nondestructive testing. A. Nachman [Ann. of Math. 143 (1996)] proved global uniqueness for the 2-D inverse conductivity problem using a constructive method of proof. Based on this proof, Siltanen, Mueller and Isaacson [Inverse Problems 16 (2000), pp.681-...

The Recently proposed Vector Approximate Message Passing (VAMP) algorithm demonstrates a great reconstruction potential at solving compressed sensing related linear inverse problems. VAMP provides high per-iteration improvement, can utilize powerful denoisers like BM3D, has rigorously defined dynamics and is able to recover signals measured by highly undersampled ill-conditioned operators. Yet,...

A new algorithm for the computation of the spectral expansion of the eigenvalues and eigenvectors of a random non-symmetric matrix is proposed. The algorithm extends the deterministic inverse power method using a spectral discretization approach. The convergence and accuracy of the algorithm is studied for both symmetric and non-symmetric matrices. The method turns out to be efficient and robus...

CHANCHAN, PRAKASH. An Algorithm for Computing the Perron Root of a Nonnegative Irreducible Matrix. (Under the direction of Carl D. Meyer.) We present a new algorithm for computing the Perron root of a nonnegative irreducible matrix. The algorithm is formulated by combining a reciprocal of the well known Collatz’s formula with a special inverse iteration algorithm discussed in [10, Linear Algebr...