W e describe the use of splines for solv-i n g n o n l i n e a r model estimation problems, in which nonlinear functions with unknown shapes and values are involved, by converting the nonlinear estimation problems into linear ones at a higher-dimensional space. This contrasts with the typical use of the splines [1]–[3] for function interpolation where the functional values at some input points ...

It is well-known that the Legendre-Fenchel conjugate of a positive-definite quadratic form can be explicitly expressed as another positive-definite quadratic form, and that the conjugate of the sum of several positive-definite quadratic forms can be expressed via inf-convolution. However, the Legendre-Fenchel conjugate of the product of two positive-definite quadratic forms is not clear at pres...

Abstract: In the present paper, the modified cubic B-spline differential quadrature method (MCB-DQM) has been implemented for the numerical computation of two-dimensional biological population model (BPM). The method is based on differential quadrature in which the weighting coefficients are computed by using MCB as a set of basis functions. We present three test problems to confirm the efficie...

Analogous to the quadratic B-spline curve, a piecewise quadratic trigonometric polynomial curve is presented in this paper. The quadratic trigonometric polynomial curve has C2 continuity, while the quadratic B-spline curve has C1 continuity. The quadratic trigonometric polynomial curve is closer to the given control polygon than the quadratic B-spline curve.

We present the construction of a multivariate normalized B-spline basis for the quadratic C-continuous spline space defined over a triangulation in R (s ≥ 1) with a generalized Powell-Sabin refinement. The basis functions have a local support, they are nonnegative, and they form a partition of unity. The construction can be interpreted geometrically as the determination of a set of s-simplices ...

A new technique and an algorithm have been designed which are meant to automatically capture the outlines of fonts. A more flexible class of B! ezier cubic (generalized Hermite cubic) functions are the basis of this technique. This class of functions involves two families of control parameters, to produce more flexible shapes than ordinary Hermite or B! ezier cubics, in each segment. These func...

This paper presents cubic spline interpolation based trajectory planning method which is aiming to achieve smooth biped robot walking trajectory. We first characterize the bipedal walking cycle and point out some major issues that need to be addressed to plan a continuous swing leg trajectory by using the concept of cubic polynomial and cubic spline interpolation. By applying these interpolatio...