In this paper, we study an inexact inverse iteration with inner-outer iterations for solving the generalized eigenvalue problem Ax = Bx; and analyze how the accuracy in the inner iterations aaects the convergence of the outer iterations. By considering a special stopping criterion depending on a threshold parameter, we show that the outer iteration converges linearly with the threshold paramete...

Building on [BB08a], we prove a general criterion for convergence of (possibly singular) Bergman measures towards equilibrium measures on complex manifolds. The criterion may be formulated in terms of growth properties of balls of holomorphic sections, or equivalently as an asymptotic minimization of generalized Donaldson L-functionals. Our result yields in particular the proof of a well-known ...

The minimum error entropy (MEE) criterion is an important learning criterion in information theoretical learning (ITL). However, the MEE solution cannot be obtained in closed form even for a simple linear regression problem, and one has to search it, usually, in an iterative manner. The fixed-point iteration is an efficient way to solve the MEE solution. In this work, we study a fixed-point MEE...

We derive a new criterion for a real-valued function u to be in the Sobolev space W 1,2(Rn). This criterion consists of comparing the value of a functional R f(u) with the values of the same functional applied to convolutions of u with a Dirac sequence. The difference of these values converges to zero as the convolutions approach u, and we prove that the rate of convergence to zero is connected...

The concept of equi-outer semicontinuity allows us to relate the pointwise and the graphical convergence of set-valued-mappings. One of the main results is a compactness criterion that extends the classical Arzelà-Ascol̀ı Theorem for continuous functions to this new setting; it also leads to the exploration of the notion of continuous convergence. Equi-lower semicontinuity of functions is relate...

We give estimates of the distance between the densities of the laws of two functionals F and G on the Wiener space in terms of the Malliavin-Sobolev norm of F −G. We actually consider a more general framework which allows one to treat with similar (Malliavin type) methods functionals of a Poisson point measure (solutions of jump type stochastic equations). We use the above estimates in order to...

Traditional discriminative training methods modify Hidden Markov Model (HMM) parameters obtained via a Maximum Likelihood (ML) criterion based estimator. In this paper, anti-models are introduced instead. The anti-models are used in tandem with ML models to incorporate a discriminative information from training data set and modify the HMM output likelihood in a discriminative way. Traditional d...

The notions of Lipschitz conditions with L average are introduced to the study of convergence analysis of Gauss-Newton’s method for singular systems of equations. Unified convergence criteria ensuring the convergence of Gauss-Newton’s method for one kind of singular systems of equations with constant rank derivatives are established and unified estimates of radii of convergence balls are also o...

Dedicated to R. T. Rockafellar on his 60th Birthday In a Banach space X, we introduce a criterion for comparing the Wijsman topologies that are induced by two equivalent norms of X on the hyperspace of closed convex sets C(X). Thereafter, we study the duality map associated with the unit ball of a given norm of X in relation to its composition with the polarity map. This more geometrical descri...

We define a general form of termination, α-termination, for term rewrite systems with an annotation α. Standard termination and top-termination are particular instances. We present a variation on the dependency pair criterion of Arts and Giesl and prove that an α-annotated term rewrite system is α-terminating if and only there are no chains of α-dependency pairs. The α-dependency graphs can be ...