Subspace Iteration Randomization and Singular Value Problems

Subspace Iteration Randomization and Singular Value Problems

A classical problem in matrix computations is the efficient and reliable approximation of a given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is known to provide the best such approximation for any given fixed rank. However, the SVD is also known to be very costly to compute. Among the different approaches in the literature for computing low-rank approxima...

Application of variational iteration method for solving singular two point boundary value problems

In this paper, He's highly prolic variational iteration method is applied ef-fectively for showing the existence, uniqueness and solving a class of singularsecond order two point boundary value problems. The process of nding solu-tion involves generation of a sequence of appropriate and approximate iterativesolution function equally likely to converge to the exact solution of the givenproblem w...

A New Inexact Inverse Subspace Iteration for Generalized Eigenvalue Problems

In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.

Value Iteration over Belief Subspace

Partially Observable Markov Decision Processes (POMDPs) provide an elegant framework for AI planning tasks with uncertainties. Value iteration is a well-known algorithm for solving POMDPs. It is notoriously difficult because at each step it needs to account for every belief state in a continuous space. In this paper, we show that value iteration can be conducted over a subset of belief space. T...

Robust recursive bi-iteration singular value decomposition (SVD) for subspace tracking and adaptive filtering