This article introduces a bivariate shape-preserving interpolation algorithm to approximate the value function of a dynamic program. First, we present a savings allocation problem between a pension account and another non-pension one. With the objective of maximizing the present value of utility over a life cycle, the investor can distribute his or her savings, in each account, between stocks a...

Linear interpolation is the computationally simplest of all possible interpolation techniques. Interestingly, it works reasonably well in many practical situations, even in situations when the corresponding computational models are rather complex. In this paper, we explain this empirical fact by showing that linear interpolation is the only interpolation procedure that satisfies several reasona...

The present paper is devoted to the development of a kind of spectral meshless radial point interpolation (SMRPI) technique in order to obtain a reliable approximate solution for buckling of nano-actuators subject to different nonlinear forces. To end this aim, a general type of the governing equation for nano-actuators, containing integro-differential terms and nonlinear forces is considered. ...

We consider the convergence of a class of reinforcement learning algorithms combined with value function interpolation methods using the methods developed in (Littman & Szepesvári, 1996). As a special case of the obtained general results, for the first time, we prove the (almost sure) convergence of Qlearning when combined with value function interpolation in uncountable spaces.

Mean value interpolation is a simple, fast, linearly precise method of smoothly interpolating a function given on the boundary of a domain. For planar domains, several properties of the interpolant were established in a recent paper by Dyken and the second author, including: sufficient conditions on the boundary to guarantee interpolation for continuous data; a formula for the normal derivative...

s for MAIA 2007 The limits of bivariate Lagrange projectors Carl de Boor∗ and Boris Shekhtman Eastsound, Washington In a talk in Norway in 2003, the first author conjectured that any finite-rank ideal projector (i.e., finite-rank linear projector on the space of polynomials in d variables whose kernel is a polynomial ideal, i.e., a linear space also closed under pointwise multiplication by poly...

1 Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA 2 Mathematics and Statistics Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia 3 Department of Mathematics, Azores University, R. Mãe de Deus, 9500-321 Ponta Delgada, Portugal 4 School of ELectrical & Electronic Engineering, Nanyang Technological University, Sin...

Corrosion in general is a complex interaction between water and metal surfaces and materials in which the water is stored or transported. Water quality monitoring in terms of corrosion and scaling is crucial, and a key element of preventive maintenance, given the economic and health hurts caused by corrosion and scaling in water utilities. The aim of this study is to determine the best model fo...

In this paper, an algorithm based on the collocation and homotopy analysis methods, for solving initial-boundary value problems, is introduced. The application of this algorithm is based on the approximation and interpolation of the dependent variables by using suitable functions or polynomials according to their values in the collocation points corresponding to a suitable discretization of the...

The general mathematical problem of fuzzy control is an interpolation problem: a list of fuzzy input-output data, usually provided by a list of linguistic control rules, should be realized as argument-value pairs for a suitably chosen fuzzy function. However, contrary to the usual understanding of interpolation, in the actual approaches this interpolation problem is considered as a global one: ...