The most common approach for approximating non-periodic function defined on a finite interval is based on considering polynomials as basis functions. In this paper we will address the non-optimallity of polynomial approximation and suggest to switch from powers of x to powers of sin(px) where p is a parameter which depends on the dimension of the approximating subspace. The new set does not suf...

fuzzy newton-cotes method for integration of fuzzy functions that was proposed by ahmady in [1]. in this paper we construct error estimate of fuzzy newton-cotes method such as fuzzy trapezoidal rule and fuzzy simpson rule by using taylor's series. the corresponding error terms are proven by two theorems. we prove that the fuzzy trapezoidal rule is accurate for fuzzy polynomial of degree one and...

A fast algorithm is developed to compute orthogonal polynomial expansions on sparse grids for a function of d variables in a weighted L space. The proposed algorithm combines the fast cosine transform, a fast transform from the Chebyshev orthogonal polynomial basis to the orthogonal polynomial basis for the weighted L space and a fast algorithm of computing hierarchically structured basis funct...

Until now, only non-oscillatory radial basis functions (RBFs) have been considered in the literature. It has recently been shown that a certain family of oscillatory RBFs based on J Bessel functions give rise to non singular interpolation problems and seem to be the only class of functions not to diverge in the limit of flat basis functions for any node layout. This paper proves another interes...

Basis functions of biquadratic polynomial spline spaces over hierarchical T-meshes are constructed. The basis functions are all tensor-product B-splines, which are linearly independent, nonnegative and complete. To make basis functions more efficient for geometric modeling, we also give out a new basis with the property of unit partition. Two preliminary applications are given to demonstrate th...

In this paper, an approach to generate surrogate models constructed by radial basis function networks (RBFN) with a priori bias is presented. RBFN as a weighted combination of radial basis functions only, might become singular and no interpolation is found. The standard approach to avoid this is to add a polynomial bias, where the bias is defined by imposing orthogonality conditions between the...

The complexity of the dual basis of a type I optimal normal basis of Fqn over Fq was determined to be 3n − 3 or 3n − 2 according as q is even or odd, respectively, by Z.-X. Wan and K. Zhou in 2007. We give a new proof to this result by clearly deriving the dual of a type I optimal basis with the aid of a lemma on the dual of a polynomial basis.

in this paper, an effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (rbfs). we present an algorithm based on interpolation by radial basis functions including multiquadratics (mqs), using legendre-gauss-lobatto nodes and weights. also a theorem is proved for convergence of the algorithm. some numerical examples are presented...

We describe the Fourier basis, a linear value function approximation scheme based on the Fourier series. We empirically demonstrate that it performs well compared to radial basis functions and the polynomial basis, the two most popular fixed bases for linear value function approximation, and is competitive with learned proto-value functions.