in this paper, an efficient method for solving optimal control problemsof the linear differential systems with inequality constraint is proposed. by usingnew adjustment of hat basis functions and their operational matrices of integration,optimal control problem is reduced to an optimization problem. also, the erroranalysis of the proposed method is investigated and it is proved that the order o...

In the present paper, a numerical method is considered for solving one-dimensional heat equation subject to both Neumann and Dirichlet initial boundary conditions. This method is a combination of collocation method and radial basis functions (RBFs). The operational matrix of derivative for Laguerre-Gaussians (LG) radial basis functions is used to reduce the problem to a set of algebraic equatio...

The recently proposed “generalized min-max” (GMM) kernel [9] can be efficiently linearized, with direct applications in large-scale statistical learning and fast near neighbor search. The linearized GMM kernel was extensively compared in [9] with linearized radial basis function (RBF) kernel. On a large number of classification tasks, the tuning-free GMM kernel performs (surprisingly) well comp...

A Bayesian framework for the analysis of radial basis functions (RBF) is proposed which readily accommodates uncertainty in the dimension of the model. A distribution is deened over the space of all RBF models of a given basis function and posteriors are computed using reversible jump Markov chain Monte Carlo samplers (Green, 1995). This alleviates the need to select one particular architecture...

The parametric or geometric continuity of a rational polynomial curve has often been obtained by requiring the homogeneous polynomial curve associated with the rational curve to possess parametric or geometric continuity, respectively. Recently this approach has been shown overly restrictive. We make use of the necessary and su cient conditions of rational parametric continuity for de ning basi...

ix Resumé xi Remerciements xiii Abbréviations xv I General Introduction 1 0.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0.2 Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 0.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 0.4 Outline . . . . . . . . . . . . . . . . . . . . ...

This chapter describes the steps involved in registering images of different subjects into roughly the same co-ordinate system, where the co-ordinate system is defined by a template image (or series of images). The method only uses up to a few hundred parameters, so can only model global brain shape. It works by estimating the optimum coefficients for a set of bases, by minimizing the sum of sq...

Polynomials suffice as finite element basis functions for triangles, parallelograms, and some other elements of little practical importance. Rational basis functions extend the range of allowed elements to the much wider class of well-set algebraic elements, where well-set is a convexity type constraint. The extension field from R(x, y) to R(x, y, √ x2 + y2) removes this quadrilateral constrain...