We construct Lagrange interpolating polynomials for a set of points and values belonging to the algebra of real quaternions $q simeq R_{0,2}$, or to the real Clifford algebra $R_{0,3}$. In the quaternionic case, the approach by means of Lagrange polynomials is new, and gives a complete solution of the interpolation problem. In the case of $R_{0,3}$, such a problem is dealt with here for the first time. Elements of the recent theory of slice regular functions are used. Leaving apart the classical cases $R_{0,0} simeqR$, $R_{0,1}simeqC$ and the trivial case $R_{1,0} simeq R oplus R$, the interpolation problem on Clifford algebras $R_{p,q}$ with $(p,q) eq (0,2),(0,3)$ seems to have some intrinsic difficulties.

Lagrange polynomials over Clifford numbers / Ghiloni, Riccardo; Perotti, Alessandro. - In: JOURNAL OF ALGEBRA AND ITS APPLICATIONS. - ISSN 0219-4988. - 14:5(2015), pp. 1550069-1-1550069-11. [10.1142/S0219498815500693]

Lagrange polynomials over Clifford numbers

Ghiloni, Riccardo;Perotti, Alessandro
2015-01-01

Abstract

We construct Lagrange interpolating polynomials for a set of points and values belonging to the algebra of real quaternions $q simeq R_{0,2}$, or to the real Clifford algebra $R_{0,3}$. In the quaternionic case, the approach by means of Lagrange polynomials is new, and gives a complete solution of the interpolation problem. In the case of $R_{0,3}$, such a problem is dealt with here for the first time. Elements of the recent theory of slice regular functions are used. Leaving apart the classical cases $R_{0,0} simeqR$, $R_{0,1}simeqC$ and the trivial case $R_{1,0} simeq R oplus R$, the interpolation problem on Clifford algebras $R_{p,q}$ with $(p,q) eq (0,2),(0,3)$ seems to have some intrinsic difficulties.
2015
5
Ghiloni, Riccardo; Perotti, Alessandro
Lagrange polynomials over Clifford numbers / Ghiloni, Riccardo; Perotti, Alessandro. - In: JOURNAL OF ALGEBRA AND ITS APPLICATIONS. - ISSN 0219-4988. - 14:5(2015), pp. 1550069-1-1550069-11. [10.1142/S0219498815500693]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/99221
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