in this work we deal with the question: how can one improve the approximation level for some nonlinear integral equations? good candidates for this aim are semi orthogonal b-spline scaling functions and their duals. although there are different works in this area, only b-spline of degree at most 2 are used for this approximation. here we compute b-spline scaling functions of degree 4 and their ...

Abstract. We study the prize-collecting version of the Node-weighted Steiner Tree problem (NWPCST) restricted to planar graphs. We give a new primal-dual Lagrangian-multiplier-preserving (LMP) 3-approximation algorithm for planar NWPCST. We then show a (2.88+ǫ)-approximation which establishes a new best approximation guarantee for planar NWPCST. This is done by combining our LMP algorithm with ...

We obtain a result concerning the stability under the interpolation with functional parameter method for the approximation spaces of LorentzMarcinkiewicz type and also for the approximation spaces generated by symmetric norming functions of a certain type.

Let $L$ be an integral and commutative quantale. In this paper, by fuzzifying the notion of generalized neighborhood systems, the notion of $L$-fuzzy generalized neighborhoodsystem is introduced and then a pair of lower and upperapproximation operators based on it are defined and discussed. It is proved that these approximation operators include generalized neighborhood system...

We study the multivariate approximation by certain partial sums (hyperbolic wavelet sums) of wavelet bases formed by tensor products of univariate wavelets. We characterize spaces of functions which have a prescribed approximation error by hyperbolic wavelet sums in terms of a K -functional and interpolation spaces. The results parallel those for hyperbolic trigonometric cross approximation of ...

This paper presents a geometric interpolation method for curve approximation in 3 R space. Given a curve, the new method is to find an approximation Bézier curve of degree 4 tangent with the given curve at the two end points and at an inner point as well. The resulting Bézier curve is explicitly expressed in the parameters of the tangent inner point of both the given curve and the approximation...