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: In this article, the generalized Hermite interpolation is derived by us- ing the contour integral and extending the generalizedHermite inter- polation to obtain the sampling expansion involving derivatives for band-limited functions.
Abstract: We derive the generalized Hermite interpolation by us- ing the contour integral and extend the generalized Hermite inter- polation to obtain the sampling expansion involving derivatives for band-limited functions f, that is, f is an entire function satisfying the following growth condition jf(z)jA exp(aejyj) for some A; ae > 0 and any z = x + iy 2C:
8 citations
TL;DR: In this article, the authors investigate the advantages in terms of shape preservation and computational efficiency of calculating univariate cubic spline fits using a steepest-descent algorithm to minimize a global data-fitting functional under a constraint implemented by a local analysis-based interpolating-spline algorithm on 5-node windows.
Abstract: $$L^1$$ splines have been under development for interpolation and approximation of irregular geometric data We investigate the advantages in terms of shape preservation and computational efficiency of calculating univariate cubic $$L^1$$ spline fits using a steepest-descent algorithm to minimize a global data-fitting functional under a constraint implemented by a local analysis-based interpolating-spline algorithm on 5-node windows Comparison of these locally calculated $$L^1$$ spline fits with globally calculated $$L^1$$ spline fits previously reported in the literature indicates that the locally calculated spline fits preserve shape on the average slightly better than the globally calculated spline fits and are computationally more efficient because the locally-calculated-spline-fit algorithm can be parallelized
8 citations
TL;DR: In this article, the algebraic structure of bivariate C^1 cubic spline spaces over nonuniform type-2 triangulation and its subspaces with boundary conditions is discussed.
Abstract: In this paper, we discuss the algebraic structure of bivariate C^1 cubic spline spaces over nonuniform type-2 triangulation and its subspaces with boundary conditions. The dimensions of these spaces are determined and their local support bases are constructed.
8 citations
Journal Article•
TL;DR: In this paper, the problem of semi-cardinal interpolation for polyharmonic splines is considered and a solution to this problem using a Lagrange series representation is presented using Fourier transforms and the technique of Wiener-Hopf factorizations for semi-space lattices.
Abstract: We consider the problem of semi-cardinal interpolation for polyharmonic splines. For absolutely summable data sequences, we construct a solution to this problem using a Lagrange series representation. The corresponding Lagrange functions are deened using Fourier transforms and the technique of Wiener-Hopf factorizations for semi-space lattices.
8 citations
8 citations