Brèves communications. Une propriété des fonctions splines d'ajustement
Calculation of Cubic Smoothing Splines for Equally Spaced Data.
Chebyshev Approximation by Spline Functions with Free Knots.
Closed spline curves bounding maximal area.
Compactly Supported Fundamental Functions for Spline Interpolation.
Computation with wavelets in higher dimensions.
Construction of surface spline interpolants of scattered data over finite domains
Convergence of approximate splines via pseudo-inverses
Cubic splines with minimal norm
Natural cubic interpolatory splines are known to have a minimal -norm of its second derivative on the (or class of interpolants. We consider cubic splines which minimize some other norms (or functionals) on the class of interpolatory cubic splines only. The cases of classical cubic splines with defect one (interpolation of function values) and of Hermite splines (interpolation of function values and first derivatives) with spline knots different from the points of interpolation are discussed....
Data approximation using polyharmonic radial basis functions
The paper is concerned with the approximation and interpolation employing polyharmonic splines in multivariate problems. The properties of approximants and interpolants based on these radial basis functions are shown. The methods of such data fitting are applied in practice to treat the problems of, e.g., geographic information systems, signal processing, etc. A simple 1D computational example is presented.
Data compression with -approximations based on splines
The paper contains short description of -algorithm for the approximation of the function with two independent variables by the sum of products of one-dimensional functions. Some realizations of this algorithm based on the continuous and discrete splines are presented here. Few examples concerning with compression in the solving of approximation problems and colour image processing are described and discussed.
Direct solution of nonlinear constrained quadratic optimal control problems using B-spline functions
In this paper, a new numerical method for solving the nonlinear constrained optimal control with quadratic performance index is presented. The method is based upon B-spline functions. The properties of B-spline functions are presented. The operational matrix of derivative () and integration matrix () are introduced. These matrices are utilized to reduce the solution of nonlinear constrained quadratic optimal control to the solution of nonlinear programming one to which existing well-developed...
Discrete Cubic Spline Interpolation
Discrete quadratic splines.
Discrete smoothing splines and digital filtration. Theory and applications
Two universally applicable smoothing operations adjustable to meet the specific properties of the given smoothing problem are widely used: 1. Smoothing splines and 2. Smoothing digital convolution filters. The first operation is related to the data vector with respect to the operations , and to the smoothing parameter . The resulting function is denoted by . The measured sample is defined on an equally spaced mesh
Dual algorithms for convex approximations of histograms using cubic C¹-splines
Efficient L2 Approximation by Splines.
Eine Aussage zur L...-Stabilität und zur genauen Konvergenzordnung der H...-Projektionen.
Error Bounds for the Approximation of Green's Kernels by Splines.
Error estimate for quadratic spline interpolating the first derivatives