1 Activity Report The two-month visit at CERFACS has been a pleasure and an exciting experience, for the opportunity to share ideas with the researchers working there, on a large variety of elds. My staying coincided with two important workshops, \Direct Methods" and \Eigenvalues and beyond" in the ILAY frame. They were both extremely valuable and it was a great opportunity for me to meet peopl...

A method, based on a semivectorial finite difference scheme, is described to construct modal fields for any twodimensional refractive-index profile which is constant except at abrupt interfaces. The modal fields correspond to eigenvectors of the matrix equation to be solved. In order to find the eigenvectors and their corresponding eigenvalues, the matrix equation is formulated according to the...

Sparse inverse synthetic aperture radar (ISAR) imaging can be generally achieved by compressed sensing (CS) methods because sparse sampling disables the approach of conventional range Doppler. However, CS-based have to convert matrix into a vector when random is adopted, which results in huge memory usage and high computational complexity. Note that completion (MC) suitable for operations, reco...

We are interested in the determination of the shape of an elastic obstacle from its effects on known incident acoustic waves. We propose a solution methodology based on a regularized Newton-type method to solve this inverse obstacle problem. At each Newton iteration, we solve the forward problems using a finite element solver based on discontinuous Galerkin approximations, and equipped with hig...

When speaking about linear programming problems of big dimensions with rare matrix of the system, solved through simplex method, it is necessary, at each iteration, to calculate the inverse of the base matrix, which leads to the loss of the rarity character of the matrix. The paper proposes the replacement of the calculus of the inverse of the base matrix with solving through iterative parallel...

We incorporate our recent preconditioning techniques into the classical inverse power (Rayleigh quotient) iteration for computing matrix eigenvectors. Every loop of this iteration essentially amounts to solving an ill conditioned linear system of equations. Due to our modification we solve a well conditioned linear system instead. We prove that this modification preserves local quadratic conver...

A new inverse iteration algorithm that can be used to compute all the eigenvectors of a real symmetric tridiagonal matrix on parallel computers is developed. In the classical inverse iteration algorithm, the modified GramSchmidt orthogonalization is used, and this causes a bottleneck in parallel computing. In this paper, the use of the compact WY representation is proposed in the orthogonalizat...

We consider and analyze applying a spectral inverse iteration algorithm and its subspace iteration variant for computing eigenpairs of an elliptic operator with random coefficients. With these iterative algorithms the solution is sought from a finite dimensional space formed as the tensor product of the approximation space for the underlying stochastic function space, and the approximation spac...

The residual inverse iteration is a simple method for solving eigenvalue problems that are nonlinear in the eigenvalue parameter. In this paper, we establish a new expression and a simple bound for the asymptotic convergence factor of this iteration in the special case that the nonlinear eigenvalue problem is Hermitian and admits a so called Rayleigh functional. These results are then applied t...

BACKGROUND Fluorescent molecular tomography (FMT) aims at reconstructing the spatial map of optical and fluorescence parameters from fluence measurements. Basically, solving large-scale matrix equations is computationally expensive for image reconstruction of FMT. Despite the reconstruction quality can be improved with more sources, it may result in higher computational costs for reconstruction...