For an invertible diagonal matrix D , the convergence of the power scaled matrix sequence N N D A  is investigated. As a special case, necessary and sufficient conditions are given for the convergence of N N D T  , where T is triangular. These conditions involve both the spectrum as well as the diagraph of the matrix T . The results are then used to privide a new proof for the convergence of ...

We present experiments with various solvers for large sparse matrix eigenvalue problems. These problems occur in the computation of a few of the lowest frequencies of standing electromagnetic waves in cavities that have been discretized by the nite element method. The solvers investigated are (1) subspace iteration, (2) block Lanczos algorithm, (3) implicitly restarted Lanczos algorithm and (4)...

This paper addresses the issue of numerical computation in machine learning domains based on similarity metrics, such as kernel methods, spectral techniques and Gaussian processes. It presents a general solution strategy based on Krylov subspace iteration and fast N-body learning methods. The experiments show significant gains in computation and storage on datasets arising in image segmentation...

This paper describes and compares several methods for computing stationary probability distributions of Markov chains. The main linear algebra problem consists of computing an eigenvector of a sparse, non-symmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous, singular linear system. We present several methods based on combinations of Kry...

For the saddle-point problems arising from the finite element discretizations of the hybrid formulations of the time-harmonic eddy current problems, we establish a class of block alternating splitting implicit iteration methods and demonstrate its unconditional convergence. Experimental results are given to show the feasibility and effectiveness of this class of iterative methods when they are ...

In this manuscript we reduce the computation of the singular values of a general product/quotient of matrices to the computation of the singular values of an upper triangular semiseparable matrix. Compared to the reduction into a bidiagonal matrix the reduction into semiseparable form exhibits a nested subspace iteration. Hence, when there are large gaps between the singular values, these gaps ...

We present an effective preconditioning technique for solving the nonsymmetric linear systems encountered in computation of incompressible flows in long domains. The application category we focus on is arterial fluid mechanics. These linear systems are solved using a nested iterative scheme with an outer Richardson scheme and an inner iteration that is handled via a Krylov subspace method. Test...

This work presents a fast and non-convex algorithm for robust subspace recovery. The data sets considered include inliers drawn around a low-dimensional subspace of a higher dimensional ambient space, and a possibly large portion of outliers that do not lie nearby this subspace. The proposed algorithm, which we refer to as Fast Median Subspace (FMS), is designed to robustly determine the underl...

We present two methods for calculating resonant frequencies and mode shapes for fluid-structure vibration problems. We model the fluid-structure interaction problem using the #-V-P, finite element technique. This eigenproblem is more complicated than for ordinary structural analyses, as the formulation produces a quadratic eigenproblem (similar to those for gyroscopic systems). We derive proper...

We propose an Approximate Implicit Subspace Iteration with Alternating Directions (AISIAD) framework for Linear Time Invariant (LTI) system model reduction. Within this framework, dominant eigensubspaces of the product of the system Gramians are approximated directly. This has advantage over approaches that consider the system Gramians separately. We construct two methods within the framework, ...