Numerical solutions are proposed to fit the CanDecomp/ParaFac (CP) model of real three-way arrays, when the latter are both nonnegative and symmetric in two modes. In other words, a seminonnegative INDSCAL analysis is performed. The nonnegativity constraint is circumvented by means of changes of variable into squares, leading to an unconstrained problem. In addition, two globalization strategie...

This paper extends the recently introduced variable step-size (VSS) approach to the family of adaptive filter algorithms. This method uses prior knowledge of the channel impulse response statistic. Accordingly, optimal stepsize vector is obtained by minimizing the mean-square deviation (MSD). The presented algorithms are the VSS affine projection algorithm (VSS-APA), the VSS selective partial u...

We consider off-policy temporal-difference (TD) learning methods for policy evaluation in Markov decision processes with finite spaces and discounted reward criteria, and we present a collection of convergence results for several gradient-based TD algorithms with linear function approximation. The algorithms we analyze include: (i) two basic forms of two-time-scale gradient-based TD algorithms,...

The Barzilai–Borwein (BB) gradient method is efficient for solving large-scale unconstrained problems to modest accuracy due its ingenious stepsize which generally yields nonmonotone behavior. In this paper, we propose a new accelerate the BB by requiring finite termination minimizing two-dimensional strongly convex quadratic function. Based on stepsize, develop an optimization adaptively takes...

It is well known that DC offset degrades the performance of analog adaptive filters. The effects of DC offset on LMS derivatives such as sign-data LMS, sign-error LMS and sign-sign LMS have been studied to much extent but that on MLMS, VSSLMS and NLMS algorithms have remained relatively ignored. The present paper reports the effects of dc offset on LMS algorithm and its four variations Sign LMS...

This paper investigates iterated Multistep Runge-Kutta methods of Radau type as a class of explicit methods suitable for parallel implementation. Using the idea of van der Houwen and Sommeijer 18], the method is designed in such a way that the right-hand side evaluations can be computed in parallel. We use stepsize control and variable order based on iterated approximation of the solution. A co...

Nonlinear evolution equations governed by m-accretive operators in Banach spaces are discretized via the backward or forward Euler methods with variable stepsize. Computable a posteriori error estimates are derived in terms of the discrete solution and data, and shown to converge with optimal order O( √ τ). Applications to scalar conservation laws and degenerate parabolic equations (with or wit...

To approximate convolutions which occur in evolution equations with memory terms, a variable-stepsize algorithm is presented for which advancing N steps requires only O(N log N) operations and O(log N) active memory, in place of O(N) operations and O(N) memory for a direct implementation. A basic feature of the fast algorithm is the reduction, via contour integral representations, to differenti...

In this paper, we propose a generic and simple algorithmic framework for first order optimization. The framework essentially contains two consecutive steps in each iteration: 1) computing and normalizing the mini-batch stochastic gradient; 2) selecting adaptive step size to update the decision variable (parameter) towards the negative of the normalized gradient. We show that the proposed approa...

A new type of variable coefficient Runge-Kutta-Nyström methods is proposed for solving the initial value problems of the special form y(t) = f(t, y(t)). The method is based on the exact integration of some given functions in order to solve the problem exactly when the solution is the linear combination of these functions. If this is not the case, the algebraic order (order of accuracy) of the m...