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 ...

Abstract This work introduces a new one-step method with three intermediate points for solving stiff differential systems. These types of problems appear in different disciplines and, particular, derived from chemical reactions. In fact, the term “stiff”’ was coined by Curtiss and Hirschfelder an article on kinetics (Hirschfelder, Proc Natl Acad Sci USA 38:235–243, 1952). The techniques interpo...

Variable-step variable-order 3-stage Hermite–Birkhoff–Obrechkoff methods of order 4 to 14, denoted by HBO(4-14)3, are constructed for solving non-stiff systems of first-order differential equations of the form y′ = f(x, y), y(x0) = y0. These methods use y′ and y′′ as in Obrechkoff methods. Forcing a Taylor expansion of the numerical solution to agree with an expansion of the true solution leads...

This paper is concerned with the numerical approximation of the expected value IE(g(Xt)), where g is a suitable test function and X is the solution of a stochastic differential equation driven by a Lévy process Y . More precisely we consider an Euler scheme or an “approximate” Euler scheme with stepsize 1/n, giving rise to a simulable variable Xn t , and we study the error δn(g) = IE(g(X n t ))...

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...

<p style='text-indent:20px;'>We study the problem of minimizing sum two functions. The first function is average a large number nonconvex component functions and second convex (possibly nonsmooth) that admits simple proximal mapping. With diagonal Barzilai-Borwein stepsize for updating metric, we propose variable metric stochastic variance reduced gradient method in mini-batch setting, na...

Most existing works use dual decomposition and first-order methods to solve Network Utility Maximization (NUM) problems in a distributed manner, which suffer from slow rate of convergence properties. This paper develops an alternative distributed Newtontype fast converging algorithm for solving NUM problems. By using novel matrix splitting techniques, both primal and dual updates for the Newton...