In this paper, we propose basic and improved algorithms based on polynomial B-spline form for constrained global optimization of multivariate functions. The proposed are a branch-and-bound framework. algorithm introduce several new ingredients, such as box consistency hull to prune the search regions make more efficient. performance is tested compared set test problems. results tests show super...

In this paper, we construct a novel normalized B-spline-like representation for C2-continuous cubic spline space defined on an initial partition refined by inserting two new points inside each sub-interval. The basis functions are compactly supported non-negative that geometrically constructed and form convex of unity. With the help control polynomial theory introduced herein, Marsden identity ...

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected].. Institute of Mathematical Statistics is collaborating wit...

In this paper we calculate the Ehrhart’s polynomial associated with a 2-dimensional regular polytope (i.e. equilateral triangles) in Z. The polynomial takes a relatively simple form in terms of the coordinates of the vertices of the triangle. We give some equivalent formula in terms of a parametrization of these objects which allows one to construct equilateral triangles with given properties. ...

Conccpts and techniques for thc construction of spline surfaces over irregular meshes are developed and made concrete by exhibiting a family of 0 2 surface splines. These splines extend the B-spline paradigm for the construction of parametric piecewise polynomial surfaces to control_meshe9 with non quadrila.leral cells and mOre or fewer Lhan four cells meeting at a point. In particular, the mes...

We propose a novel approach for the approximate parameterization of an implicitly defined curve in the plane by polynomial parametric spline curves. The method generates the parameterization of the curve (which may consist of several open and closed branches) without using any a priori information about its topology. If needed the topology of the approximate parameterization can be certified ag...

This paper presents a new segmentation algorithm by tting active contour models (or snakes) to objects using adaptive splines. The adaptive spline model describes the contour of an object by a set of piecewisely interpolating C 2 polynomial spline patches which are locally controlled. Thus the resulting description of the object contour is continuous and smooth. Polynomial splines provide a fas...

In this paper, we study polynomial spline collocation methods applied to a particular class of integral-algebraic equations of Volterra type. We analyse mixed systems of second and first kind integral equations. Global convergence and local superconvergence results are established.

A general theory of quasi-interpolants based on trigonometric splines is developed which is analogous to the polynomial spline case. The aim is to construct quasi-interpolants which are local, easy to compute, and which apply to a wide class of functions. As examples, we give a detailed treatment including error bounds for two classes which are especially useful in practice.

Consider a family of functions of a single variable x: Φ(x; a0, a1, . . . , an), where a0, . . . , an are the parameters. The problem of interpolation for Φ can be stated as follows: Given n + 1 real or complex pairs of numbers (xi, fi), i = 0, . . . , n, with xi 6= xk for i 6= k, determine a0, . . . , an such that Φ(xi; a0, . . . , an) = fi, i = 0, . . . , n. The above is a linear interpolatio...