Algorithms, Convergence and Rate of Convergence for an Interpolation Model Between Lagrange and Hermite

Berriochoa, E.; Cachafeiro, A.; García-Amor, J.

doi:10.1007/s00025-018-0802-0

Cited by 2 publications

(6 citation statements)

References 4 publications

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“…Also, this is particularly for differentiable functions. The results are similar to those obtained in [14] when considering the Chebyshev-Lobatto system. Section 2.7 is devoted to presenting some numerical experiments where distinct nodal systems satisfying the separation property and mechanical models are employed.…”

Section: Introductionsupporting

confidence: 88%

“…Taking into account that Proof. As we proceed as in the previous proposition, we write F(z) = F 1,n (z) + F 2,n (z) + F 3,n (z), where F 1,n (z), F 2,n (z), and F 3,n (z) are those given in (14). Since H − 3n 2 , 3n…”

Section: Convergence Of Hermite-fejér and Hermite Interpolation In Th...mentioning

confidence: 99%

“…Finally, we use the same arguments as those of Theorem 6 in [14] in the following way: We know that for an n large enough, there exists N = E[…”

Section: The Case Of the Bounded Intervalmentioning

confidence: 99%

“…In some recent papers, we considered another variation of the classical methods. Indeed, in [14,15], we studied a problem of interpolation between those of Lagrange and Hermite. There, we use all the nodes for the data values and half of them for the derivative values.…”

Section: Introductionmentioning

confidence: 99%

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A Type of Interpolation between Those of Lagrange and Hermite That Uses Nodal Systems Satisfying Some Separation Properties

Berriochoa,

Cachafeiro,

García Rábade

et al. 2024

Mathematics

Self Cite

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In this paper, we study a method of polynomial interpolation that lies in-between Lagrange and Hermite methods. The novelty is that we use very general nodal systems on the unit circle as well as on the bounded interval only characterized by a separation property. The way in which we interpolate consists in considering all the nodes for the prescribed values and only half for the derivatives. Firstly, we develop the theory on the unit circle, obtaining the main properties of the nodal polynomials and studying the convergence of the interpolation polynomials corresponding to continuous functions with some kind of modulus of continuity and with general conditions on the prescribed values for half of the derivatives. We complete this first part of the paper with the study of the convergence for smooth functions obtaining the rate of convergence, which is slightly slower than that when equidistributed nodal points are considered. The second part of the paper is devoted to solving a similar problem on the bounded interval by using nodal systems having good properties of separation, generalizing the Chebyshev–Lobatto system, and well related to the nodal systems on the unit circle studied before. We obtain an expression of the interpolation polynomials as well as results about their convergence in the case of continuous functions with a convenient modulus of continuity and, particularly, for differentiable functions. Finally, we present some numerical experiments related to the application of the method with the nodal systems dealt with.

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Section: Introductionsupporting

confidence: 88%

Section: Convergence Of Hermite-fejér and Hermite Interpolation In Th...mentioning

confidence: 99%

“…Finally, we use the same arguments as those of Theorem 6 in [14] in the following way: We know that for an n large enough, there exists N = E[…”

Section: The Case Of the Bounded Intervalmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Type of Interpolation between Those of Lagrange and Hermite That Uses Nodal Systems Satisfying Some Separation Properties

Berriochoa,

Cachafeiro,

García Rábade

et al. 2024

Mathematics

Self Cite

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show abstract

“…The common interpolation methods include linear interpolation, Lagrange interpolation, spline interpolation [14,15]. In actual engineering, Lagrange twopoint interpolation, Lagrange three-point quadratic interpolation (parabolic interpolation) and least squares approximation should be selected if the number of measuring points and test accuracy need to be considered [16].…”

Section: Course Effect Errormentioning

confidence: 99%

Design and Software Implementation of a Navigation Accuracy Evaluation Based on Error Model Solution

Huang¹,

Yi²,

Zeng³

et al. 2019

I2M

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This paper attempts to improve the accuracy of navigation accuracy evaluation of inertial navigation system (INS). Firstly, the course effect error of the INS was analyzed in details. Then, the errors of inertial devices like gyro and accelerometer were modelled separately. Based on these models, the author simulated how the course effect error and the second-order errors related to the specific force (SF2Es) affect the speed error, position error and attitude error of the INS, under two trajectory conditions. Based on the solution of the models, a navigation accuracy evaluation software was developed, which can evaluate one or more INSs at the same time. The research findings lay the theoretical basis for INS navigation accuracy evaluation.

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Algorithms, Convergence and Rate of Convergence for an Interpolation Model Between Lagrange and Hermite

Cited by 2 publications

References 4 publications

A Type of Interpolation between Those of Lagrange and Hermite That Uses Nodal Systems Satisfying Some Separation Properties

A Type of Interpolation between Those of Lagrange and Hermite That Uses Nodal Systems Satisfying Some Separation Properties

Design and Software Implementation of a Navigation Accuracy Evaluation Based on Error Model Solution

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