Optimal Vector Smoothing Splines with Coupled Constraints

Smoothing under Diffeomorphic Constraints with Homeomorphic Splines

In this paper we introduce a new class of diffeomorphic smoothers based on general spline smoothing techniques and on the use of some tools that have been recently developed in the context of image warping to compute smooth diffeomorphisms. This diffeomorphic spline is defined as the solution of an ordinary differential equation governed by an appropriate time-dependent vector field. This solut...

Nonparametric fixed-interval smoothing with vector splines

Optimal trajectory planning and smoothing splines

In this paper, some of the relationships between optimal control and trajectory planning are examined. When planning trajectories for linear control systems, a demand that arises naturally in air tra$c control or noise contaminated data interpolation is that the curve passes close to given points, or through intervals, at given times. In this paper, we produce these curves by solving an optimal...

Smoothing with Cubic Splines

A spline function is a curve constructed from polynomial segments that are subject to conditions or continuity at their joints. In this paper, we shall present the algorithm of the cubic smoothing spline and we shall justify its use in estimating trends in time series. Considerable effort has been devoted over several decades to developing the mathematics of spline functions. Much of the intere...

Fast computation of smoothing splines subject to equality constraints

The issue of constructing periodic smoothing splines has been recently formulated as a controlled two point boundary value problem which admits a state-space description. In the context of minimum norm problems in Hilbert spaces, it has been shown that the solution is the sum of a finite number of basis functions and can be obtained with a number of operations which scales with the cube of the ...