This paper presents formulas for constructing quadratic minimal splines, which explicitly depend on the components of a generating vector function. Formulas various approximation functionals splines used as coefficients in local methods are obtained. Examples special cases schemes, known quasi-interpolation, provided. Results numerical experiments approximating circular arc by considered.

This paper describes the problem of shape preserving approximation for data with speci ed tolerances Using the tool of generalized B splines GB splines for short simple one and three point algorithms of shape preserving local approximation with automatic choice of the tension parameters are de veloped In the two dimensional case tensor products of one dimensional splines are employed The result...

[Her13] F.Hernoux, R.Béarée, L.Gajny, E.Nyiri, J.Bancalin, O.Gibaru, Leap Motion pour la capture de mouvement 3D par spline L1. Application à la robotique. GTMG 2013, Marseille, 27-28 mars 2013 [Gib1899] J. Willard Gibbs, lettre à l’éditeur, Nature 59 (April 27, 1899) 606. [Lav00] J.E. Lavery, Univariate Cubic Lp splines and shape-preserving multiscale interpolation by univariate cubic L1 splin...

Splines, which were invented by Schoenberg more than fifty years ago, constitute an elegant framework for dealing with interpolation and discretization problems. They are widely used in computer-aided design and computer graphics, but have been neglected in medical imaging applications, mostly as a consequence of what one may call the "bad press" phenomenon. Thanks to some recent research effor...

We review recently developed methods of constructing Lagrange and Her-mite interpolation sets for bivariate splines on triangulations of general type. Approximation order and numerical performance of our methods are also discussed.

Bounds are provided on how well functions in Sobolev spaces on the sphere can be approximated by spherical splines, where a spherical spline of degree d is a C r function whose pieces are the restrictions of homogoneous polynomials of degree d to the sphere. The bounds are expressed in terms of appropriate seminorms deened with the help of radial projection, and are obtained using appropriate q...

numerical solutions obtained by the meshless local petrov–galerkin (mlpg) method are presented for two-dimensional steady-state heat conduction problems. the mlpg method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. the penalty method is adopted to efficiently enforce the essential boundary co...

The original theory of splines grew out of the study of simple variational problems. A spline was a function that minimized some notion of energy subject to a set of interpolation constraints. A more recent method for creating splines is subdivision. A spline is the limit of a sequence of functions, each related by some simple averaging rule. This paper shows that the two ideas are intrinsicall...

Fuzzy rule interpolation is an important technique for performing inferences with sparse rule bases. Even when given observations have no overlap with the antecedent values of any rule, fuzzy rule interpolation may still derive a conclusion. Nevertheless, fuzzy rule interpolation can only handle fuzziness but not roughness. Rough set theory is a useful tool to deal with incomplete knowledge, wh...

The aim of this paper is to introduce a novel two-step Fuzzy Rule Interpolation Technique (FRIT) “VEIN”, based on the concept of Vague Environment. The strength of FRIT against classical fuzzy reasoning methods is the ability of gaining conclusion even in case where the knowledge is represented by sparse fuzzy rule bases. The FRIT “VEIN” introduced in this paper is following the structure the G...