We present an approach for the acceleration of the restarted Arnoldi iteration for the computation of a number of eigenvalues of the standard eigenproblem Ax = x. This study applies the Chebyshev polynomial to the restarted Arnoldi iteration and proves that it computes necessary eigenvalues with far less complexity than the QR method. We also discuss the dependence of the convergence rate of th...

The cyclic block coordinate descent-type (CBCD-type) methods, which performs iterative updates for a few coordinates (a block) simultaneously throughout the procedure, have shown remarkable computational performance for solving strongly convex minimization problems. Typical applications include many popular statistical machine learning methods such as elastic-net regression, ridge penalized log...

Value iteration is a commonly used and em­ pirically competitive method in solving many Markov decision process problems. However, it is known that value iteration has only pseudo­ polynomial complexity in general. We estab­ lish a somewhat surprising polynomial bound for value iteration on deterministic Markov decision (DMDP) problems. We show that the basic value iteration procedure converges...

Value iteration is a commonly used and empirically competitive method in solving many Markov decision process problems. However, it is known that value iteration has only pseudopolynomial complexity in general. We establish a somewhat surprising polynomial bound for value iteration on deterministic Markov decision (DMDP) problems. We show that the basic value iteration procedure converges to th...

A special kind of substitution on languages called iteration is presented and studied. These languages arise in the application of semantic automata to iterations of generalized quantifiers. We show that each of the star-free, regular, and deterministic context-free languages are closed under iteration and that it is decidable whether a given regular or determinstic context-free language is an ...

Dearing and Zeck [5] presented a dual algorithm for the problem of the minimum covering ball in R. Each iteration of their algorithm has a computational complexity of at least O(n). In this paper we propose a modification to their algorithm that, together with an implementation that uses updates to the QR factorization of a suitable matrix, achieves a O(n) iteration.

The cyclic block coordinate descent-type (CBCD-type) methods have shown remarkable computational performance for solving strongly convex minimization problems. Typical applications includes many popular statistical machine learning methods such as elastic-net regression, ridge penalized logistic regression, and sparse additive regression. Existing optimization literature has shown that the CBCD...

The block preconditioned steepest descent iteration is an iterative eigensolver for subspace eigenvalue and eigenvector computations. An important area of application of the method is the approximate solution of mesh eigenproblems for self-adjoint and elliptic partial differential operators. The subspace iteration allows to compute some of the smallest eigenvalues together with the associated i...

Existing multi-kernel tracking methods are based on a forwards additive motion model formulation. However this approach suffers from the need to estimate an update matrix for each iteration. This paper presents a general framework that extends the existing approach and that allows to introduce a new inverse compositional formulation which shifts the computation of the update matrix to a one tim...