In reference to a self-referential approach towards smooth multivariate approximation

Pandey, K. K.; Viswanathan, P.

doi:10.1007/s11075-022-01261-7

Cited by 3 publications

(4 citation statements)

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“…In this section we provide a quick proof of Theorem, as an alternative to the proof given in [1]. In addition to the already defined H k a (x), we define the following…”

Section: An Alternative Quick Proof Of Theorem 12mentioning

confidence: 99%

“…denotes the rounding to the nearest integer (round) operator. , namely t (0,0) (0,0) , t (0,0) (1,0) , t (0,0) (0,1) , t (0,0) (1,1) at each one of the support points, as well as the values of the partial derivatives up to the 1st degree: t (0,1) (0,0) , t (0,1) (1,0) , t (0,1) (0,1) , t (0,1) (1,1) , t (1,0) (0,0) , t (1,0) (1,0) , t (1,0) (0,1) , t (1,0) (1,1) , t (1,1) (0,0) , t (1,1) (1,0) , t (1,1) (0,1) , t (1,1) (1,1) , the following conditions must hold:…”

Section: Hermite Splines Interpolation Approachmentioning

confidence: 99%

“…To our knowledge, the only n-dimensional multivariate generalization of the 1D classical Hermite interpolation in Spitzbart [5] was proposed very recently in [1], and it is presented in the following Theorem:…”

Section: Introduction and Notationsmentioning

confidence: 99%

“…First, we prove the uniqueness of the interpolating polynomial, and we further obtain a compact closed form that uses a single summation, irrespective of the dimensionality. The arithmetic complexity of the derived closed formula compares favourably with the only alternative closed form for the n-dimensional classical Hermite interpolation [1]. In addition, we provide the remainder of the interpolation.…”

mentioning

confidence: 99%

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Classical multivariate Hermite coordinate interpolation in n-dimensional grid

Kechriniotis¹,

Delibasis²,

Oikonomou³

et al. 2023

Preprint

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In this work, we study the Hermite interpolation on n-dimensional non-equal spaced, rectilinear grids over a field k of characteristic zero, given the values of the function at each point of the grid and the partial derivatives up to a maximum degree. First, we prove the uniqueness of the interpolating polynomial, and we further obtain a compact closed form that uses a single summation, irrespective of the dimensionality. The arithmetic complexity of the derived closed formula compares favourably with the only alternative closed form for the n-dimensional classical Hermite interpolation [1]. In addition, we provide the remainder of the interpolation. Finally, we perform illustrative numerical examples to showcase the applicability and high accuracy of the proposed interpolant, compared to other interpolation methods.

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“…In this section we provide a quick proof of Theorem, as an alternative to the proof given in [1]. In addition to the already defined H k a (x), we define the following…”

Section: An Alternative Quick Proof Of Theorem 12mentioning

confidence: 99%