Let \(\mathbb {K}\) be a commutative field, \(p, n \in \mathbb {N}^*\) , \(Z_n\) be a triangle in \(\mathbb {K}^{p}\) of size n, where n denotes the number of points aligned along each side of the triangle and \(R_n=[r_z,\; z\in Z_n]\) be an interpolation data. It is known that there exists a unique polynomial P of total degree less than or equal to n (SIAM Rev. 61, 361–381, 2019), satisfying \( P (Z_n) = R_n, \text { that is, } P (z) = r_{z} ,\ z \in Z_n. \) Recently, Errachid et al. (Numer. Algorithms 84, 1507–1534, 2020) presented a new algorithm for computing the Lagrange multivariate interpolation polynomial in a particular case where the interpolation set is a rectangular grid called the Recursive MultiVariate Polynomial Interpolation Algorithm (RMVPIA). In this paper, we propose another approach to studying the problem of Lagrange multivariate polynomial interpolation in a particular case where the interpolation set is a triangular grid and derive a new algorithm, called the Triangular Recursive Lagrange Multivariate Polynomial Interpolation Algorithm (TRLMPIA), for \(p = 2\) and \(p = 3\) . A simplified version of this algorithm will also be studied and some examples will be given.
