On integro quartic spline interpolation

Lang, Feng-Gong; Xu, Xiaoping

doi:10.1016/j.cam.2012.05.017

Cited by 29 publications

(38 citation statements)

References 8 publications

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“…In this paper, an effort that is different from the ones in [1,2,[13][14][15][16][17][18][19] is made to construct a new kind of integro quintic spline without exact end conditions. The demands of exact end conditions in many old methods, such as [1,2,14,15,18], for integro interpolation have been relaxed and deleted in the new method.…”

Section: Discussionmentioning

confidence: 99%

“…From (13), it follows that M 0 = y 0 = y 0 + O(h 5 ). Moreover, by using (37), (42), (43) and (45), we have:…”

Section: Approximation Propertiesmentioning

confidence: 99%

“…The problem arises in many fields, such as numerical analysis, mathematical statistics, environmental science, mechanics, electricity, climatology, oceanography, and so on. We refer to [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] for its applied backgrounds and some recent developments.…”

Section: Introductionmentioning

confidence: 99%

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A New Quintic Spline Method for Integro Interpolation and Its Error Analysis

Lang

2017

Algorithms

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Abstract:In this paper, to overcome the innate drawbacks of some old methods, we present a new quintic spline method for integro interpolation. The method is free of any exact end conditions, and it can reconstruct a function and its first order to fifth order derivatives with high accuracy by only using the given integral values of the original function. The approximation properties of the obtained integro quintic spline are well studied and examined. The theoretical analysis and the numerical tests show that the new method is very effective for integro interpolation.

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Section: Discussionmentioning

confidence: 99%

“…From (13), it follows that M 0 = y 0 = y 0 + O(h 5 ). Moreover, by using (37), (42), (43) and (45), we have:…”

Section: Approximation Propertiesmentioning

confidence: 99%

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A New Quintic Spline Method for Integro Interpolation and Its Error Analysis

Lang

2017

Algorithms

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“…In the course of preparing our manuscript, we were informed of other spline interpolation techniques that conserve intensity (Delhez 2003;Lang and Xu 2012). As far as we are aware, no routines based on these techniques are publicly available.…”

Section: Discussionmentioning

confidence: 99%

Intensity Conserving Spectral Fitting

2015

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The detailed shapes of spectral line profiles provide valuable information about the emitting plasma, especially when the plasma contains an unresolved mixture of velocities, temperatures, and densities. As a result of finite spectral resolution, the intensity measured by a spectrometer is the average intensity across a wavelength bin of non-zero size. It is assigned to the wavelength position at the center of the bin. However, the actual intensity at that discrete position will be different if the profile is curved, as it invariably is. Standard fitting routines (spline, Gaussian, etc.) do not account for this difference, and this can result in significant errors when making sensitive measurements. Detection of asymmetries in solar coronal emission lines is one example. Removal of line blends is another. We have developed an iterative procedure that corrects for this effect. It can be used with any fitting function, but we employ a cubic spline in a new analysis routine called Intensity Conserving Spline Interpolation (ICSI). As the name implies, it conserves the observed intensity within each wavelength bin, which ordinary fits do not. Given the rapid convergence, speed of computation, and ease of use, we suggest that ICSI be made a standard component of the processing pipeline for spectroscopic data.

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“…Delhez [11], F.G. Lang and X.P. Xu [18] and T. Zhanlav and R. Mijiddorj [19]. In these papers it was necessary to suppose that the function f had several derivatives and error estimations were not given in some of them.…”

Section: 1mentioning

confidence: 99%

Uniform reconstruction of continuous functions with the RAFU method

Cortés¹

2017

Appl. Gen. Topol.

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The RAFU (radical functions) method can be used to obtain the uniform reconstruction of a continuous function from its values at some of the points of partitions of a closed interval. In this work we will prove that we can reconstruct a continuous function from average samples of these points, from linear combinations of them and from local average samples given by convolution. A uniform error bound of order O h 3 2 ) + ω (h) with the step size h will be established. If these data are unknown but approximate values of them are known, uniform reconstruction will be also possible. Error estimates of order O h 3 2 + ω (h) + η with noise level η will be given. The case of a non-uniform net will be treated. Examples and algorithms will be also shown.

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On integro quartic spline interpolation

Cited by 29 publications

References 8 publications

A New Quintic Spline Method for Integro Interpolation and Its Error Analysis

A New Quintic Spline Method for Integro Interpolation and Its Error Analysis

Intensity Conserving Spectral Fitting

Uniform reconstruction of continuous functions with the RAFU method

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