Cubic splines with minimal norm
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In this paper, the authors consider cubic splines which minimize some other norms (or functionals) on the class of interpolatory cubic spline only, and the cases of classical cubic interpolatory splines with defect one and Hermite C1 splines (interpolation of function values and first derivatives) with spline knots different from the points of interpolation are discussed.Abstract:
Natural cubic interpolatory splines are known to have a minimal L2-norm of its second derivative on the C2 (or W22) 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 C1 splines (interpolation of function values and first derivatives) with spline knots different from the points of interpolation are discussed.read more
Citations
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Journal ArticleDOI
Fitting data using optimal Hermite type cubic interpolating splines
TL;DR: The existence and uniqueness of the Hermite type cubic spline with minimal quadratic oscillation in average are proved and a new optimal property for cubic interpolating splines of Hermitetype applied to data-fitting problems is obtained.
Journal ArticleDOI
Cubic Hermite interpolation with minimal derivative oscillation
TL;DR: A new optimal cubic Hermite interpolation method is presented to optimize the derivative of the interpolant and the diagonally dominant property of the obtained system of normal equations and the error bound are better than some of the existing cubic interpolants.
Journal ArticleDOI
Optimizing at the end-points the Akima's interpolation method of smooth curve fitting ☆
TL;DR: An optimized version of the Akima's interpolation method for experimental data fitting, at the end-points, of the Catmull–Rom's cubic spline is proposed, and the error estimate is improved.
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Deficient quartic spline of Marsden type with minimal deviation by the data polygon
TL;DR: In this paper , the authors constructed the deficient quartic spline with the knots following the Marsden's scheme and proved its existence and uniqueness with minimal deviation by the data polygon.
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New interpolation paradigm for the design of ship profile
Alexandru Mihai Bica,Eugen Laslo +1 more
References
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Book
A practical guide to splines
TL;DR: This book presents those parts of the theory which are especially useful in calculations and stresses the representation of splines as linear combinations of B-splines as well as specific approximation methods, interpolation, smoothing and least-squares approximation, the solution of an ordinary differential equation by collocation, curve fitting, and surface fitting.
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Numerical Methods for Least Squares Problems
TL;DR: Theorems and statistical properties of least squares solutions are explained and basic numerical methods for solving least squares problems are described.
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Solving differential problems by multistep initial and boundary value methods
Luigi Brugnano,Donato Trigiante +1 more
TL;DR: This paper presents a meta-modelling framework for generalized backward Differentiation Formulae, and some of the methods used in this framework have been adapted for practical use in the reinforcement learning environment.