High order approximation by CCC-spline quasi-interpolants

Numerical computation using splines (65D07) Best approximation, Chebyshev systems (41A50) Rate of convergence, degree of approximation (41A25) Approximation by operators (in particular, by integral operators) (41A35) Spline approximation (41A15) Algorithms for approximation of functions (65D15) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Cites Work

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A shape-preserving approximation by weighted cubic splines
On the critical lengths of cycloidal spaces
Quadratic convergence of approximations by CCC-Schoenberg operators
Quasi-interpolation in isogeometric analysis based on generalized B-splines
Finding all systems of weight functions associated with a given extended Chebyshev space
A collocation method for singularly perturbed two-point boundary value problems with splines in tension
Chebyshev--Schoenberg operators
Quadratic spline quasi-interpolants and collocation methods
Interpolation on cycloidal spaces
Interpolation by generalized splines
Chebyshevian splines: interpolation and blossoms
Collocation by singular splines
The general recurrence relation for divided differences and the general Newton-interpolation-algorithm. With applications to trigonometric interpolation
Local spline approximation methods
On Tschebycheffian spline functions
Piecewise Chebyshevian splines: interpolation versus design
Fitted mesh \(B\)-spline collocation method for solving self-adjoint singularly perturbed boundary value problems
Spline approximation by quasiinterpolants
Critical length for design purposes and extended Chebyshev spaces
Sharp error bounds for interpolating splines in tension
de Boor-fix dual functionals and algorithms for Tchebycheffian B-spline curves
Piecewise Chebyshev-Schoenberg operators: shape preservation, approximation and space embedding
Variable degree polynomial splines are Chebyshev splines
Isogeometric collocation methods with generalized B-splines
A practical method for computing with piecewise Chebyshevian splines
Tchebycheffian B-splines revisited: an introductory exposition
Critical length: an alternative approach
Application of CCC-Schoenberg operators on image resampling
Design or not design? A numerical characterisation for piecewise Chebyshevian splines
Non-uniform exponential tension splines
One sided Hermite interpolation by piecewise different generalized polynomials
A collocation method for boundary value problems
Tchebycheffian B-splines in isogeometric Galerkin methods
A Collocation Method for Two-Point Boundary Value Problems
A Tchebycheffian Extension of Multidegree B-Splines: Algorithmic Computation and Properties
Algorithm 1020: Computation of Multi-Degree Tchebycheffian B-Splines
Collocation at Gaussian Points
A fourth/second order accurate collocation method for singularly perturbed two-point boundary value problems using tension splines
A practical guide to splines.

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