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 from partition of unity methods. ...

An algorithm for sequential approximation with optimal coefficients and interacting frequencies (SAOCIF) for feed-forward neural networks is presented. SAOCIF combines two key ideas. The first one is the optimization of the coefficients (the linear part of the approximation). The second one is the strategy to choose the frequencies (the non-linear weights), taking into account the interactions ...

We build on the classical greedy sequential set cover algorithm, in the spirit of the primal-dual schema, to obtain simple parallel approximation algorithms for the set cover problem and its generalizations. Our algorithms use randomization, and our randomized voting lemmas may be of independent interest. Fast parallel approximation algorithms were known before for set cover, though not for the...

Wattenhofer et al. [WW04] derive a complicated distributed algorithm to compute a weighted matching of an arbitrary weighted graph, that is at most a factor 5 away from the maximum weighted matching of that graph. We show that a variant of the obvious sequential greedy algorithm [Pre99], that computes a weighted matching at most a factor 2 away from the maximum, is easily distributed. This yiel...

Psychological experiments have shown that human performance on traditional causal reasoning experiments can be greatly influenced by different pretraining and postraining conditions. In this paper we present a Bayesian theory of sequential learning that captures observed experimental results [1] . We implement our theory using the particle filter algorithm, and show that model selection and mod...

In this paper, we propose an arc-search corrector-predictor interior-point method for solving $P_*(kappa)$-linear complementarity problems. The proposed algorithm searches the optimizers along an ellipse that is an approximation of the central path. The algorithm generates a sequence of iterates in the wide neighborhood of central path introduced by Ai and Zhang. The algorithm does not de...

in this article we implement an operational matrix of fractional integration for legendre polynomials. we proposed an algorithm to obtain an approximation solution for fractional differential equations, described in riemann-liouville sense, based on shifted legendre polynomials. this method was applied to solve linear multi-order fractional differential equation with initial conditions, and the...

We provide a new constant factor approximation algorithm for the (connected) distance-r dominating set problem on graph classes of bounded expansion. Classes of bounded expansion include many familiar classes of sparse graphs such as planar graphs and graphs with excluded (topological) minors, and notably, these classes form the most general subgraph closed classes of graphs for which a sequent...

This paper considers the computation of matrix chain products of the form M1 M2 Mn?1. The order in which the matrices are multiplied aaects the number of operations. The best sequential algorithm for computing an optimal order of matrix multiplication runs in O(n log n) time while the best known parallel NC algorithm runs in O(log 2 n) time using n 6 = log 6 n processors. This paper presents th...

The lack of focus that is a characteristic of unsupervised pattern mining in sequential data represents one of the major limitations of this approach. This lack of focus is due to the inherently large number of rules that is likely to be discovered in any but the more trivial sets of sequences. Several authors have promoted the use of constraints to reduce that number, but those constraints app...