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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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Journal ArticleDOI
Song-Tao Liu1
TL;DR: The additive Schwarz‐type preconditioner for fourth‐order elliptic problems with nested subspaces from Hermite cubic splines is constructed and it is proved that after the preconditionsing, the system is well conditioned.
Abstract: In this note, we construct the additive Schwarz-type preconditioner for fourth-order elliptic problems with nested subspaces from Hermite cubic splines. We prove that after the preconditioning, the system is well conditioned. The numerical evidence strongly supports our theoretical result. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006

4 citations

Journal ArticleDOI
TL;DR: Due to the generally monotonic nature of the dipole moment surface, the one-part weight function is found to be more effective than the more complicated two-part variant, with first-order interpolation also giving better-than-expected results.
Abstract: We outline an approach for building molecular dipole moment surfaces using modified Shepard interpolation. Our approach is highly automated, requires minimal parameterization, and is iteratively improvable. Using the water molecule as a test case, we investigate how different aspects of the interpolation scheme affect the rate of convergence of calculated IR spectral line intensities. It is found that the interpolation scheme is sensitive to coordinate singularities present at linear geometries. Due to the generally monotonic nature of the dipole moment surface, the one-part weight function is found to be more effective than the more complicated two-part variant, with first-order interpolation also giving better-than-expected results. Almost all sensible schemes for choosing interpolation reference data points are found to exhibit acceptable convergence behavior.

4 citations

Journal ArticleDOI
TL;DR: A cubic spline method for the numerical solution of a two-point boundary value problem posed on an infinite interval involving a second-order linear differential equation is described in this article, where the stability of the method is analyzed and the theory is illustrated by solving test examples.

4 citations

Proceedings ArticleDOI
28 Aug 2005
TL;DR: Overall performance of three pass algorithms is better than two pass algorithms as they have no signal contraction and interpolation can be obtained by convolution.
Abstract: This paper analyses two-dimensional image rotation algorithms on the basis of execution time and mean square error produced. Effect of forward and reverse mapping on algorithm complexity is discussed. Single and multipass algorithms have been analyzed. Various interpolation techniques including nearest neighbor, linear, cubic, sinc and cubic spline interpolation are applied to the problem of image rotation. Sinc and cubic spline produce good quality images but are computationally intensive and are not suitable for real time rotation applications. Overall performance of three pass algorithms is better than two pass algorithms as they have no signal contraction and interpolation can be obtained by convolution. The real time rotation algorithms were implemented on MDSP architecture for X-ray images.

4 citations

Posted Content
TL;DR: Pchipolate as discussed by the authors uses piecewise cubic Hermite interpolation of missing values of yvar, given xvar, and the piecewise cubics join smoothly, so that both the interpolated function and its first derivative are continuous.
Abstract: pchipolate creates newvar by averaging non-missing values of yvar and using piecewise cubic Hermite interpolation of missing values of yvar, given xvar. This method is often described informally as "pchip". The piecewise cubics join smoothly, so that both the interpolated function and its first derivative are continuous. In addition, the interpolant is shape-preserving in the sense that it cannot overshoot locally; sections in which observed yvar is increasing, decreasing or constant with xvar remain so after interpolation, and local extremes (maxima, maxima) also remain so.

3 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202316
202227
20191
201812
201740
201652