In this paper, we consider the construction of a new class of numerical methods based on the backward differentiation formulas (BDFs) that be equipped by including two off--step points. We represent these methods from general linear methods (GLMs) point of view which provides an easy process to improve their stability properties and implementation in a variable stepsize mode. These superioritie...

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...

We describe an extension of the Taylor method for numerical solution ODEs that uses Padé approximants to obtain extremely precise results. The accuracy results is essentially limited only by computer time and memory, provided one works in arbitrary precision. In this stepsize adjusted achieve desired (variable stepsize), while order expansion can be either fixed or changed at each iteration ord...

Numerical difficulties encountered when following paths using methods such as homotopy continuation may be overcome by combining adaptive stepsize and adaptive multiprecision. In the paper Adaptive multiprecision path tracking [1], precision and stepsize are adapted separately. This can lead to suboptimal performance and even failure in certain circumstances. This paper presents a strategy for ...

Modulus Algorithms for Blind Equalization Constantinos B. Papadias e-mail: [email protected] Dirk T. M. Slock e-mail: [email protected] Institut EURECOM, 2229 route des Crêtes, Sophia Antipolis, 06560 Valbonne, FRANCE Abstract One of the most known classes of algorithms for blind equalization is the so-called class of Constant Modulus Algorithms (CMA's) [1], [2]. These adaptive algorithms use ...

The affine-scaling algorithm, first proposed by Dikin, is presently enjoying great popularity as a potentially effective means of solving linear programs. An outstanding question about this algorithm is its convergence in the presence of degeneracy (which is important since 'practical" problems tend to be degenerate). In this paper, we give new convergence results for this algorithm that do not...

This paper discusses efficient simulation methods for stochastic chemical kinetics. Based on the tau-leap and midpoint tau-leap methods of Gillespie [D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001)], binomial random variables are used in these leap methods rather than Poisson random variables. The motivation for this approach is to improve the efficiency of the Poisson leap methods by using la...