The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform

Yekini Shehu - One of the best experts on this subject based on the ideXlab platform.

  • strong Convergence Result of forward backward splitting methods for accretive operators in banach spaces with applications
    Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-matematicas, 2018
    Co-Authors: Yekini Shehu, Gang Cai
    Abstract:

    Our interest in this paper is to prove strong Convergence Results for finding zeros of the sum of two accretive operators by utilizing a viscosity type forward–backward splitting method. We also discuss applications of this method to approximation of solution to certain integro-differential equation with generalized p-Laplacian operator. Our Results complement many recent and important Results in the literature.

  • strong Convergence Result for proximal split feasibility problem in hilbert spaces
    Optimization, 2017
    Co-Authors: Yekini Shehu, Olaniyi S. Iyiola
    Abstract:

    AbstractIn this paper we describe and analyse new computational technique for solving proximal split feasibility problem (SFP) using a modified proximal split feasibility algorithm. The two convex and lower semi-continuous objective functions are assumed to be non-smooth. Some application to SFP are given. We demonstrate the computational efficiency of the proposed algorithm with nontrivial numerical experiments. We also compare our method with other relevant methods in the literature in terms of Convergence, stability, efficiency and implementation with our illustrative numerical examples.

  • Strong Convergence Result for monotone variational inequalities
    Numerical Algorithms, 2017
    Co-Authors: Yekini Shehu, Olaniyi S. Iyiola
    Abstract:

    Our aim in this paper is to study strong Convergence Results for L -Lipschitz continuous monotone variational inequality but L is unknown using a combination of subgradient extra-gradient method and viscosity approximation method with adoption of Armijo-like step size rule in infinite dimensional real Hilbert spaces. Our Results are obtained under mild conditions on the iterative parameters. We apply our Result to nonlinear Hammerstein integral equations and finally provide some numerical experiments to illustrate our proposed algorithm.

  • a strong Convergence Result involving an inertial forward backward algorithm for monotone inclusions
    Journal of Fixed Point Theory and Applications, 2017
    Co-Authors: Qiaoli Dong, Yekini Shehu, Dan Jiang, Prasit Cholamjiak
    Abstract:

    Our interest in this paper is to prove a strong Convergence Result for finding a zero of the sum of two monotone operators, with one of the two operators being co-coercive using an iterative method which is a combination of Nesterov’s acceleration scheme and Haugazeau’s algorithm in real Hilbert spaces. Our numerical Results show that the proposed algorithm converges faster than the un-accelerated Haugazeau’s algorithm.

Neri Merhav - One of the best experts on this subject based on the ideXlab platform.

Terence P Speed - One of the best experts on this subject based on the ideXlab platform.

  • a rate of Convergence Result for a universal d semifaithful code
    IEEE Transactions on Information Theory, 1993
    Co-Authors: Terence P Speed
    Abstract:

    The problem of optimal rate universal coding is considered in the context of rate-distortion theory. A D-semifaithful universal coding scheme for discrete memoryless sources is given. The main Result is a refined covering lemma based on the random coding argument and the method of types. The average codelength of the code is shown to approach its lower bound, the rate-distortion function, at a rate O(n/sup -1/log n), and this is conjectured to be optimal based on a Result of A.J. Pilc (1968). Issues of constructiveness and universality are addressed. >

Luc Devroye - One of the best experts on this subject based on the ideXlab platform.

  • another proof of a slow Convergence Result of birge
    Statistics & Probability Letters, 1995
    Co-Authors: Luc Devroye
    Abstract:

    We give a short proof of the following Result. Let fn be any density estimate based upon an i.i.d. sample drawn from a density f. For any monotone decreasing sequence {an} of positive numbers converging to zero with , a density f may be found such that for all n. This density may be picked from the class of densities on [0, 1] that are bounded by two. The proof of this fact simplifies an earlier proof by Birge (1986) and extends a weaker lower bound by the author (1983).

  • Another proof of a slow Convergence Result of Birgé
    Statistics & Probability Letters, 1995
    Co-Authors: Luc Devroye
    Abstract:

    Abstract We give a short proof of the following Result. Let fn be any density estimate based upon an i.i.d. sample drawn from a density f. For any monotone decreasing sequence {an} of positive numbers converging to zero with a 1 ⩽ 1 32 , a density f may be found such that E ∫|f n (x)−f(x)| d x ⩾a n for all n. This density may be picked from the class of densities on [0, 1] that are bounded by two. The proof of this fact simplifies an earlier proof by Birge (1986) and extends a weaker lower bound by the author (1983).

Noureddine El Karoui - One of the best experts on this subject based on the ideXlab platform.

  • a rate of Convergence Result for the largest eigenvalue of complex white wishart matrices
    Annals of Probability, 2006
    Co-Authors: Noureddine El Karoui
    Abstract:

    It has been recently shown that if X is an n×N matrix whose entries are i.i.d. standard complex Gaussian and l1 is the largest eigenvalue of X*X, there exist sequences mn,N and sn,N such that (l1−mn,N)/sn,N converges in distribution to W2, the Tracy–Widom law appearing in the study of the Gaussian unitary ensemble. This probability law has a density which is known and computable. The cumulative distribution function of W2 is denoted F2. In this paper we show that, under the assumption that n/N→ γ∈(0, ∞), we can find a function M, continuous and nonincreasing, and sequences μn,N and σn,N such that, for all real s0, there exists an integer N(s0, γ) for which, if (n∧N)≥N(s0, γ), we have, with ln,N=(l1−μn,N)/σn,N, ∀ s≥s0 (n∧N)2/3|P(ln,N≤s)−F2(s)|≤M(s0)exp(−s). The surprisingly good 2/3 rate and qualitative properties of the bounding function help explain the fact that the limiting distribution W2 is a good approximation to the empirical distribution of ln,N in simulations, an important fact from the point of view of (e.g., statistical) applications.

  • a rate of Convergence Result for the largest eigenvalue of complex white wishart matrices
    arXiv: Probability, 2004
    Co-Authors: Noureddine El Karoui
    Abstract:

    It has been recently shown that if $X$ is an $n\times N$ matrix whose entries are i.i.d. standard complex Gaussian and $l_1$ is the largest eigenvalue of $X^*X$, there exist sequences $m_{n,N}$ and $s_{n,N}$ such that $(l_1-m_{n,N})/s_{n,N}$ converges in distribution to $W_2$, the Tracy--Widom law appearing in the study of the Gaussian unitary ensemble. This probability law has a density which is known and computable. The cumulative distribution function of $W_2$ is denoted $F_2$. In this paper we show that, under the assumption that $n/N\to \gamma\in(0,\infty)$, we can find a function $M$, continuous and nonincreasing, and sequences $\tilde{\mu}_{n,N}$ and $\tilde{\sigma}_{n,N}$ such that, for all real $s_0$, there exists an integer $N(s_0,\gamma)$ for which, if $(n\wedge N)\geq N(s_0,\gamma)$, we have, with $l_{n,N}=(l_1-\tilde{\mu}_{n,N})/\tilde{\sigma}_{n,N}$, \[\forall s\geq s_0\qquad (n\wedge N)^{2/3}|P(l_{n,N}\leq s)-F_2(s)|\leq M(s_0)\exp(-s).\] The surprisingly good 2/3 rate and qualitative properties of the bounding function help explain the fact that the limiting distribution $W_2$ is a good approximation to the empirical distribution of $l_{n,N}$ in simulations, an important fact from the point of view of (e.g., statistical) applications.