Inverse iteration is known to be an effective method for computing eigenvectors corresponding simple and well-separated eigenvalues. In the non-symmetric case, solution of shifted Hessenberg systems a central step. Existing inverse solvers approach with either RQ or LU factorizations and, once factored, solve systems. This has limited level-3 BLAS potential since distinct shifts have factorizat...

A class of hybrid heterogeneous methods using time implicit backward differences and Crank-Nicolson approximating schemes in conjunction with explicit domain decomposition approximate inverse matrix techniques is introduced for computing various families of approximate inverses based on approximate LU-type factorization techniques. Explicit preconditioned conjugate gradient type schemes in conj...

In this paper, we examine deflation-based algebraic multigrid methods for solving large systems of linear equations. Aggregation the unknown terms is applied coarsening, while deflation techniques are proposed improving rate convergence. More specifically, V-cycle strategy adopted, in which, at each iteration, solution computed by initially decomposing it utilizing two complementary subspaces. ...

The paper considers the inversion of full matrices whose inverses are -banded. We derive a nested inversion algorithm for such matrices. Applied to a tridiagonal matrix, the algorithm provides its explicit inverse as an element-wise product (Hadamard product) of three matrices. When related to Gauss–Markov random processes (GMrp), this result provides a closed-form factored expression for the c...

We describe an approximate dynamic programming algorithm for partially observable Markov decision processes represented in factored form. Two complementary forms of approximation are used to simplify a piecewise linear and convex value function, where each linear facet of the function is represented compactly by an algebraic decision diagram. ln one form of approximation, the degree of state ab...

Most HMM-based speech recognition systems use Gaussian mixtures as observation probability density functions. An important goal in all such systems is to improve parsimony. One method is to adjust the type of covariance matrices used. In this work, factored sparse inverse covariance matrices are introduced. Based on U DU factorization, the inverse covariance matrix can be represented using line...

This paper investigates Factored Markov Decision Processes with Imprecise Probabilities (MDPIPs); that is, Factored Markov Decision Processes (MDPs) where transition probabilities are imprecisely specified. We derive efficient approximate solutions for Factored MDPIPs based on mathematical programming. To do this, we extend previous linear programming approaches for linear approximations in Fac...

Predictive state representations (PSRs) are models that represent the state of a dynamical system as a set of predictions about future events. The existing work with PSRs focuses on trying to learn exact models, an approach that cannot scale to complex dynamical systems. In contrast, our work takes the first steps in developing a theory of approximate PSRs. We examine the consequences of using ...