For the Hermitian inexact Rayleigh quotient iteration (RQI), we present general convergence results, independent of iterative solvers for inner linear systems. We prove that the method converges quadratically at least under a new condition, called the uniform positiveness condition. This condition can be much weaker than the commonly used one that at outer iteration k, requires the relative res...

We discuss the convergence property of the minimum residual (MINRES) method for the solution of complex shifted Hermitian system (αI + H)x = f . Our convergence analysis shows that the method has a faster convergence than that for real shifted Hermitian system (Re(α)I +H)x = f under the condition Re(α) + λmin(H) > 0, and a larger imaginary part of the shift α has a better convergence property. ...

Minimum residual methods such as the least-squares finite element method (FEM) or discontinuous Petrov--Galerkin with optimal test functions (DPG) usually exclude singular data, e.g., non square-integrable loads. We consider a DPG and FEM for Poisson problem. For both we analyze regularization approaches that allow use of $H^{-1}$ loads, also study case point all cases prove appropriate converg...

The basic idea of exploratory factor analysis is the following. For a given set of observed response variables one wants to find a set of latent factors, fewer in number than the observed variables. These factors are supposed to account for the intercorrelations of the response variables in the sense that when the factors are partialed out from the observed variables, there should no longer rem...

Different preconditioning techniques for the iterative method MinRes as solver for the Discrete Sources Method (DSM) are presented. This semi-analytical method is used for light scattering computations by particles in the Mie scattering regime. Its numerical schema includes a linear least-squares problem commonly solved using the QR decomposition method. This could be the subject of numerical d...

Incomplete LDL∗ factorizations sometimes produce an inde nite preconditioner even when the input matrix is Hermitian positive de nite. The two most popular iterative solvers for Hermitian systems, MINRES and CG, cannot use such preconditioners; they require a positive de nite preconditioner. We present two new Krylov-subspace solvers, a variant of MINRES and a variant of CG, both of which can b...