A simultaneous perturbation stochastic approximation (SPSA) method has been developed in this paper, using the operators of perturbation with the Lipschitz density function. This model enables us to use the approximation of the objective function by twice differentiable functions and to present their gradients by volume integrals. The calculus of the stochastic gradient by means of this present...

Let G be a reflexive subspace of the Banach space E and let L(I, E) denote the space of all p-Bochner integrable functions on the interval I=[0, 1] with values in E, 1 [ pO.. Given any norm N(· , · ) on R, N nondecreasing in each coordinate on the set R +, we prove that L (I, G) is N-simultaneously proximinal in L(I, E). Other results are also obtained. © 2002 Elsevier Science (USA)

We apply Padé approximation techniques to deduce lower bounds for simultaneous rational approximation to one or more algebraic numbers. In particular, we strengthen work of Osgood, Fel’dman and Rickert, proving, for example, that max {∣∣∣√2− p1/q∣∣∣ , ∣∣∣√3− p2/q∣∣∣} > q−1.79155 for q > q0 (where the latter is an effective constant). Some of the Diophantine consequences of such bounds will be d...

267 Word count: 4996 Text + 6 Tables + 7 Figures = 8,246 Submission Date: August 1, 2007 Paper submitted for Presentation and Publication in the TRANSPORTATION RESEARCH RECORD, JOURNAL OF TRANSPORTATION RESEARCH BOARD AFTER BEING PRESENTED TRANSPORTATION RESEARCH BOARD’S 87 ANNUAL MEETING, WASHINGTON, D.C., 2008 TRB 2008 Annual Meeting CD-ROM Original paper submittal not revised by author.

Recently, close connections have been established between simultaneous diophantine approximation and algebraic independence. A survey of this topic is given by M. Laurent in these proceedings [7]. These connections are one of the main motivations to investigate systematically the question of algebraic approximation to transcendental numbers. In view of the applications to algebraic independence...

May [4] estimated some direct and inverse results for certain combinations of these operators. Very recently Finta and Gupta [1] studied some direct and inverse results for the second-order Ditzian-Totik modulus of smoothness. The rates of convergence in ordinary approximation for function of bounded variation for these operators and similar types of operators were estimated in [2, 3, 7]. Very ...

We study the construction of a quadrature rule which allows the simultaneous integration of a given function with respect to different weights. This construction is built on the basis of simultaneous Padé approximation of a Nikishin system of functions. The properties of these approximants are used in the proof of convergence of the quadratures and positivity of the corresponding quadrature coe...

This paper is concerned with the problem of nonlinear simultaneous Chebyshev approximation in a real continuous function space. Some results on existence are established, in addition to characterization conditions of Kolmogorov type and also of alternation type. Applications are given to approximation by rational functions, by exponential sums and by Chebyshev splines with free knots.  2003 El...