The spline collocation method  is employed to solve a system of linear and nonlinear Fredholm and Volterra integro-differential equations. The solutions are collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. We obtain the unique solution for linear and nonlinear system $(nN+3n)times(nN+3n)$ of integro-differential equations. This approximation reduces th...

A constructive approach is adopted to build B-spline like basis for cubic spline curves with a more general continuity than beta-continuity. This method provides not only a large variety of very interesting shape controls like biased, point, and interval tensions but, as a special case, also recovers a number of spline methods like nu-spline of Nielson[9], beta-splines[1], gamma-splines of Boeh...

We propose a new regularization method called Loco-Spline for nonparametric function estimation. Loco-Spline uses a penalty which is data driven and locally adaptive. This allows for more flexible estimation of the function in regions of the domain where it has more curvature, without over fitting in regions that have little curvature. This methodology is also transferred into higher dimensions...

Pottmann et al. propose an iterative optimization scheme for approximating a target curve with a B-spline curve based on square distance minimization, or SDM. The main advantage of SDM is that it does not need a parameterization of data points on the target curve. Starting with an initial B-spline curve, this scheme makes an active B-spline curve converge faster towards the target curve and pro...

We present a new multivariate spline using mixed partial derivatives. We show the existence and uniqueness of the proposed multivariate spline problem, and propose a simple finite element approximation.