Multivariate spline functions, B-spline bases and polynomial interpolations II
Natural and smoothing quadratic spline. (An elementary approach)
For quadratic spine interpolating local integrals (mean-values) on a given mesh the conditions of existence and uniqueness, construction under various boundary conditions and other properties are studied. The extremal property of such's spline allows us to present an elementary construction and an algorithm for computing needed parameters of such quadratic spline smoothing given mean-values. Examples are given illustrating the results.
New algorithms and techniques for computing with geometrically continuous spline curves of arbitrary degree
Note on symmetric alteration of knots of B-spline curves.
Numerical model of a pine in a wind
Steady-state nonlinear differential equations govering the stem curve of a wind-loaded pine are derived and solved numerically. Comparison is made between the results computed and the data from photographs of a pine stem during strong wind. The pine breaking is solved at the end.
Numerical solution of initial and singularly perturbed two-point boundary value problems using adaptive spline function approximation.
Obtaining a banded system of equations in complete spline interpolation problem via B-spline basis
We study the problem of interpolation by a complete spline of 2n − 1 degree given in B-spline representation. Explicit formulas for the first nand the last ncoefficients of B-spline decomposition are found. It is shown that other B-spline coefficients can be computed as a solution of a banded system of an equitype linear equations.
On algorithms for parabolic splines
On Best Cubature Formulas and Spline Interpolation.
On optimal nodal splines and their applications.
On smoothing conditions of multivariate splines.
On the control net of certain multivariate spline functions
On the Convergence of Interpolating Periodic Spline Functions of High Degree.
On the error estimation in numerical methods
On the numerical solution of an Abel integral equation
On the smoothing spline regression models.
On the two dimensional spline interpolation of Hermite-type.
Optimal discrete approximation of continuous linear operators applicable to control problems
Optimal interpolatory splines using -spline representation
Optimal quadratic interpolatory splines on general knotset