In a recent Math. Program. paper, Eckstein and Silva proposed a new error criterion for the approximate solutions of augmented Lagrangian subproblems. Based on a saddle-point formulation of the primal and dual problems, they autors proved that dual sequences generated by augmented Lagrangians under this error criterion are bounded and that theirs limit points are dual solutions. In this note, w...

Assume that one has to estimate a density f on R e from X1, ..., Xn, a sequence of independent random vectors with common density f A density estimate is a sequence (f,) of Borel measurable mappings: R a ( n + ~ R ; for fixed n, f (x) is estimated by f,~(x)=f,(x, X 1 . . . . , X,). In this note, we take a look at the rate of convergence of E(~ ]f , (x)f (x) lPdx) ( p > l ) for all density estim...

A convergence criterion for the Monte Carlo estimates will be proposed which can be used as a stopping rule for the Monte Carlo experiments. The proposed criterion searches a convergence band of a given width and length such that the probability of the Monte Carlo sample variance to fall outside of this band is practically null. After the convergence to the process variance realized according t...

In this note we use the boundary classification of diffusions in order to derive a criterion for the convergence of perpetual integral functionals of transient real-valued diffusions. We present a second approach, based on Khas’minskii’s lemma, which is applicable also to spectrally negative Lévy processes. In the particular case of transient Bessel processes, our criterion agrees with the one ...

In this paper we study the structure of the Banach space K(E, F) of all compact linear operators between two Banach spaces E and F. We study three distinct problems: weak compactness in K(E, F), subspaces isomorphic to l~ and complementation of K(E, F) in L(E, F), the space of bounded linear operators. In § 2 we derive a simple characterization of the weakly compact subsets of K(E, F) using a c...

Article history: Received 2 September 2008 Received in revised form 23 October 2008 Accepted 4 November 2008 Available online 13 November 2008 MSC: 65H10 65J15 47H30

A convergence criterion of the family of Euler-Halley type methods for the vector fields on Riemannian manifolds whose covariant derivatives satisfy the γ-condition is established. The corresponding results due to [12] are extended. An application to analytic vector fields is provided.

We give a convergence criterion for stationary iterative schemes based on subproper splittings for solving rectangular systems and show that, for special splittings, convergence and quotient convergence are equivalent. We also analyze the convergence of multisplitting algorithms for the solution of rectangular systems when the coefficient matrices have special properties and the linear systems ...

This paper is devoted to the investigation of the investigation of the convergence of iterative methods for solving boundary va.!ue problems with discontinuous coeficients. The dependence of the rate" of convergence on the size of the discontinuity of coefficients is ana.!yzed for three popular genera.! iterative methods. A new criterion on the applicability of such methods is proposed and inve...

A reaction-diffusion stereo algorithm consists of multi-sets of reaction-diffusion equations. Since the equations are described with time-evolving partialdifferential equations, they require much computation time. In addition, the previous algorithm does not state any criterion for convergence judgement; we need to compute the equations for enough duration of time until their solutions converge...