In [4] the authors proposed a collocation algorithm for approximating the minimal norm least-squares solution of first kind integral equations with continuous reproducing kernel. The convergence of the approximate solutions sequence is proved under the assumption that all the sets of collocation functions are linearly independent. In this paper we replace the above assumption by a weaker one an...

Moment-sum-of-squares hierarchies of semidefinite programs can be used to approximate the volume of a given compact basic semialgebraic set K. The idea consists of approximating from above the indicator function of K with a sequence of polynomials of increasing degree d, so that the integrals of these polynomials generate a convergence sequence of upper bounds on the volume of K. We show that t...

An extended notion of a local empirical process indexed by functions is introduced, which includes kernel density and regression function estimators and the conditional empirical process as special cases. Under suitable regularity conditions a central limit theorem and a strong approximation by a sequence of Gaussian processes are established for such processes. A compact law of the iterated lo...

We first recall some properties of infinite tridiagonal matrices considered as matrix transformations in sequence spaces of the forms sξ , sξ , s (c) ξ , or lp(ξ). Then, we give some results on the finite section method for approximating a solution of an infinite linear system. Finally, using a quasi-Newton method, we construct a sequence that converges fast to a solution of an infinite linear ...

In this paper, we study two new methods for approximating the viability kernel of a given set for a HH olderian diierential inclusion. We approximate this kernel by viability kernels for discrete dynam-ical systems. We prove a convergence result when the diierential inclusion is replaced by a sequence of recursive inclusions. Furthermore , when the given set is approached by a sequence of suita...

We first recall some properties of infinite tridiagonal matrices considered as matrix transformations in sequence spaces of the forms sξ , sξ , s (c) ξ , or lp(ξ). Then, we give some results on the finite section method for approximating a solution of an infinite linear system. Finally, using a quasi-Newton method, we construct a sequence that converges fast to a solution of an infinite linear ...

This paper deals with the approximation of Nash-equilibria in m-player games. We present conditions under which an approximating sequence of games admits near-equilibria that approximate near equilibria in the limit game. We apply the results to two classes of games: (i) a duopoly game approximated by a sequence of matrix games; (ii) a stochastic game played under the S-adapted information stru...

In this paper we consider a step function characterized by an arbitrary sequence of real-valued scalars and approximate it with matching pursuit (MP) algorithm. We utilize waveform dictionary rectangular window functions as part show that the is not necessary when all are either non positive or negative parameters wavelet on integer lattice yields closed-form solution for initial optimization p...

Abstract We consider the Lidstone–Euler interpolation problem and associated boundary value problem, in both theoretical computational aspects. After a theorem of existence uniqueness solution to we present numerical method for solving it. This uses extrapolated Bernstein polynomials produces an approximating convergent polynomial sequence. Particularly, fourth-order case, arising various physi...

Particle filters are numerical methods for approximating the solution of the filtering problem which use systems of weighted particles that (typically) evolve according to the law of the signal process. These methods involve a corrective/resampling procedure which eliminates the particles that become redundant and multiplies the ones that contribute most to the resulting approximation. The corr...