Topic
Monotone cubic interpolation
About: Monotone cubic interpolation is a research topic. Over the lifetime, 1740 publications have been published within this topic receiving 38111 citations.
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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.
32 citations
TL;DR: In this paper, a bivariate osculatory interpolation polynomial was developed which not only agrees with f(x, y) in function values at each of the node points of a Cartesian grid but also enjoys the property that agreement in values of partial and mixed partial derivatives up to specified, arbitrary orders is obtainable at these points.
Abstract: One of the most commonly used methods for deriving formulas for bivariate interpolation is that of extending to two variables the formulas of Lagrange, Aitken, Newton, Gauss, Stirling, Everett, Bessel, etc., in which forward, backward and central-differences are used. These formulas have the property that the resultinig interpolation polynomial agrees with the interpolated function, f(x, y), at each of the node points of a Cartesian grid. In this study, we shall investigate the existence of a wider class of interpolation formulas, together with their associated error terms, than those obtainable by the method just described. To this end, we develop a bivariate osculatory interpolation polynomial which not only agrees with f(x, y) in function values at each of the node points of a Cartesian grid but which also enjoys the property that agreement in values of partial and mixed partial derivatives up to specified, arbitrary orders is obtainable at these points. The result is essentially a bivariate generalization of Hermite's interpolation formula.
32 citations
TL;DR: In this paper, a numerical method for solving the renewal equation is proposed, which generates a cubic spline approximation of the renewal function by the Galerkin technique, tested on Gamma lifetime densities of various shapes.
Abstract: A numerical method for solving the renewal equation is proposed. The method which generates a cubic spline approximation of the renewal function by the Galerkin technique is tested on Gamma lifetime densities of various shapes. Results are compared against known analytical solutions and earlier approximation.
32 citations
TL;DR: In this paper, a method is presented for fitting a bivariate cubic spline function to values of a dependent variable, specified at points on a rectangular grid in the plane of the independent variables.
32 citations
TL;DR: In this paper, the characterization of a bi-center problem and shortened expressions of the first six Liapunov constants are completely discussed for the planar Z2-equivariant cubic systems having two elementary focuses.
Abstract: For the planar Z2-equivariant cubic systems having two elementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Liapunov constants are completely discussed. The necessary and sufficient conditions for the existence of the bi-center are obtained. All possible first integrals are given. Under small Z2-equivariant cubic perturbations, the conclusion that there exist at most 12 small-amplitude limit cycles with the scheme 〈6 ∐ 6〉 is proved.
32 citations