Tensor Interpolation

In this paper, we develop a new Lagrange tensor interpolation. We define tensorial jordanisation which gives us a practical method to calculate the coefficients of our tensor interpolating polynomial. Unlike what happens in the case of matrices where the product is simpler, there are multiple tensor...

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Vydáno v:	Numerical algorithms Ročník 100; číslo 4; s. 1599 - 1615
Hlavní autoři:	Ouahidi, Salma, Sadaka, Rachid
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.12.2025 Springer Nature B.V
Témata:	Algebra Algorithms Computer Science Fourier transforms Interpolation Numeric Computing Numerical Analysis Polynomials Tensors Theory of Computation Interpolation T-product Tensor Lagrange
ISSN:	1017-1398, 1572-9265
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Abstract	In this paper, we develop a new Lagrange tensor interpolation. We define tensorial jordanisation which gives us a practical method to calculate the coefficients of our tensor interpolating polynomial. Unlike what happens in the case of matrices where the product is simpler, there are multiple tensorial products; we use the T -product and develop a new product which is most suitable for our work, we determine the coefficients of our interpolating polynomial as well as give the expression of the Langrange tensor interpolating polynomial. Furthermore, we will give examples of the effectiveness of this method in interpolating tensorial functions.
AbstractList	In this paper, we develop a new Lagrange tensor interpolation. We define tensorial jordanisation which gives us a practical method to calculate the coefficients of our tensor interpolating polynomial. Unlike what happens in the case of matrices where the product is simpler, there are multiple tensorial products; we use the T -product and develop a new product which is most suitable for our work, we determine the coefficients of our interpolating polynomial as well as give the expression of the Langrange tensor interpolating polynomial. Furthermore, we will give examples of the effectiveness of this method in interpolating tensorial functions. In this paper, we develop a new Lagrange tensor interpolation. We define tensorial jordanisation which gives us a practical method to calculate the coefficients of our tensor interpolating polynomial. Unlike what happens in the case of matrices where the product is simpler, there are multiple tensorial products; we use the T-product and develop a new product which is most suitable for our work, we determine the coefficients of our interpolating polynomial as well as give the expression of the Langrange tensor interpolating polynomial. Furthermore, we will give examples of the effectiveness of this method in interpolating tensorial functions.
Author	Sadaka, Rachid Ouahidi, Salma
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Cites_doi	10.1016/j.jat.2015.06.006 10.1512/iumj.1981.30.30027 10.1016/0024-3795(78)90026-5 10.3390/math8081298 10.1016/0024-3795(94)90005-1 10.1007/978-3-0348-6558-6 10.1137/110837711 10.1080/03081088208817483 10.1016/j.laa.2010.09.020 10.1007/s10589-020-00231-w 10.1016/0377-0427(83)90008-0
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SubjectTerms	Algebra Algorithms Computer Science Fourier transforms Interpolation Numeric Computing Numerical Analysis Polynomials Tensors Theory of Computation
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