The local volatility function is approximated using two different models: a bicubic spline and High Dimensional Model Representation (HDMR) model. For a bicubic spline the local volatility values σi at a chosen discrete set of knots are determined by minimizing the least square error between market and model option prices. Model option prices are found using the one-factor diffusion process for...

Polycube G-splines form a 2-manifold guided by a mesh of quadrilateral faces such that at most six quads meet at each vertex. In particular, this replicates the layout of the quad faces of a polycube. Polycube G-splines are piecewise bicubic and polycube Gspline surfaces are almost everywhere tangent-continuous (G) based on rational linear reparameterization. They can be constructed in two diff...

This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel B-splines are introduced to compute a C 2 -continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarse-tofine hierarchy of control lattices to generate a sequence of bicubic B-spline functions whose sum approaches the desired interpolation function. Large p...

The paper presents numerical modeling of the dynamics of recently developed electromagnetic valve actuator. The decoupled modelling approach is employed consisting of three-dimensional finite element analysis of the magnetic field of the actuator and solution of the dynamics equations on the basis of functions obtained from the magnetic field analysis. For the finite element analysis ANSYS prog...

Bicubic maps are in bijection with β(0, 1)-trees. We introduce two new ways of decomposing β(0, 1)-trees. Using this we define an endofunction on β(0, 1)-trees, and thus also on bicubic maps. We show that this endofunction is in fact an involution. As a consequence we are able to prove some surprising results regarding the joint equidistribution of certain pairs of statistics on trees and maps....

We study the linear space of C-smooth isogeometric functions defined on a multi-patch domain Ω ⊂ R. We show that the construction of these functions is closely related to the concept of geometric continuity of surfaces, which has originated in geometric design. More precisely, the C-smoothness of isogeometric functions is found to be equivalent to geometric smoothness of the same order (G-smoot...

In this paper we present an approximation method of surfaces by a new type of splines, which we call fairness bicubic splines, from a given Lagrangian data set. An approximating problem of surface is obtained by minimizing a quadratic functional in a parametric space of bicubic splines. The existence and uniqueness of this problem are shown as long as a convergence result of the method is estab...