Interpolation by integro quintic splines

Behforooz, Hossein

doi:10.1016/j.amc.2010.01.009

Cited by 24 publications

(35 citation statements)

References 6 publications

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“…There have been only a few research papers to deal with these problems; see for example, H. Behforooz [1,2], E.J.M. Delhez [11], F.G. Lang and X.P.…”

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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“…There have been only a few research papers to deal with these problems; see for example, H. Behforooz [1,2], E.J.M. Delhez [11], F.G. Lang and X.P.…”

Section: 1mentioning

confidence: 99%

Uniform reconstruction of continuous functions with the RAFU method

Cortés¹

2017

Appl. Gen. Topol.

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“…In this paper, we will mainly focus on the quintic spline methods; see [2,14,[17][18][19] for the existing ones.…”

Section: Introductionmentioning

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%

“…The method was very complicated because it mainly required solving two linear systems. Furthermore, besides the integral values (2), the method must use seven additional exact end conditions in terms of y(x 0 ), y (x 0 ), y (x 1 ), y (x n−1 ), y (x n ), y (x 0 ) and y (x n ). Later, a new algorithm was given in [18] to simplify the construction of integro quintic spline.…”

Section: Introductionmentioning

confidence: 99%

“…The method in [2] was based on the quintic Hermite-Birkhoff polynomials. The method was very complicated because it mainly required solving two linear systems.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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On algebraic trigonometric integro splines

Eddargani

Lamnii

2019

Z Angew Math Mech

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In this paper, we present a new kind of quadratic approximation operator reproducing of both algebraic and trigonometric functions. It is called integro quadratic splines interpolant, which agree with the given integral values of a univariate real-valued function over the same intervals, rather than the functional values at the knots. Efficient approximations of fractional integrals and fractional Caputo derivatives based on this interpolant, are constructed and well studied. The general approximation error is studied too, and the super convergence property is also derived when the interval is equally partitioned. Numerical examples illustrate that our method is very effective and our quadratic algebraic trigonometric integro spline has higher approximation ability than others. K E Y W O R D Salgebraic trigonometric splines, error bound, fractional caputo derivatives, fractional integrals, integro spline quasi-interpolant

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Interpolation by integro quintic splines

Cited by 24 publications

References 6 publications

Uniform reconstruction of continuous functions with the RAFU method

Uniform reconstruction of continuous functions with the RAFU method

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

On algebraic trigonometric integro splines

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