A method of constructing a Chebyshev approximation multivariable functions by generalized polynomial with the exact reproduction its values at given points is proposed. It based on sequential construction mean-power approximations, taking into account interpolation condition. The calculated using an iterative scheme least squares variable weight function. An algorithm for calculating parameters...

This paper reconsiders sequential Monte Carlo approaches to Bayesian inference in the light of massively parallel desktop computing capabilities now well within the reach of individual academics. It first develops an algorithm that is well suited to parallel computing in general and for which convergence results have been established in the sequential Monte Carlo literature but that tends to re...

Given a dataset of points in a metric space and an integer k, a diversity maximization problem requires determining a subset of k points maximizing some diversity objective measure, e.g., the minimum or the average distance between a pair of points in the subset. Diversity maximization problems are computationally hard, hence only approximate solutions can be hoped for. Although its application...

1. Introduction. In this article we consider a class of adaptive multilevel domain decomposition-like algorithms, built from a combination of adaptive multilevel finite element, domain decomposition, and partition of unity methods. These algorithms have several interesting features such as very low communication requirements, and they inherit a simple and elegant approximation theory framework ...

Traditionally, interest in parallel computation centered around the speedup provided by parallel algorithms over their sequential counterparts. In this paper, we ask a di erent type of question: Can parallel computers, due to their speed, do more than simply speed up the solution to a problem? We show that for real-time optimization problems, a parallel computer can obtain a solution that is be...

The computation of matchings has applications in the solving process of a large variety of problems, e.g. as part of graph partitioners. We present and analyze three sequential and two parallel approximation algorithms for the cardinality and weighted matching problem. One of the sequential algorithms is based on an algorithm by Karp and Sipser to compute maximal matchings [21]. Another one is ...

Several sequential approximation algorithms are based on the following paradigm: solve a linear or semideenite programming relaxation , then use randomized rounding to convert fractional solutions of the relaxation into integer solutions for the original combinatorial problem. We demonstrate that such a paradigm can also yield parallel approximation algorithms by showing how to convert certain ...

Proving termination of sequential programs is an important problem, both for establishing the total correctness of systems and as a component of proving more general termination and liveness properties. We present a new algorithm, TREX, that determines if a sequential program terminates on all inputs. The key characteristic of TREX is that it alternates between refining an overapproximation and...

Fault detection and failure prediction for nonlinear non-Gaussian systems is an important issue both from the economic and safety point of view. Most of the fault detection techniques assume the system model to be linear and the noise to be Gaussian. These linearization assumptions tend to suffer form poor detection and imprecise prediction. Also, they may lead to false alarms which would incur...