The problems of univariate polynomial interpolation of Lagrange or Hermite have been treated by several recent researches (Gasca and Lopez-Carmona J. Approx. Theory. 34 361–374 1982; Messaoudi et al. Numer. Algorithms J 80, 253–278 2019; Messaoudi and Sadok Numer. Algorithms J 76, 675–694 2017; Muhlbach Numer. Math. 31, 97–110 1978). The study of the multivariate polynomial interpolation is more difficult and the approaches are less obvious (Gasca and Lopez-Carmona J. Approx. Theory. 34, 361–374 1982; Gasca and Sauer 2000; Lorentz 2000; Muhlbach Numer. Math. 31, 97–110 1978; Neidinger Siam Rev. 61, 361–381 2019). In Gasca and Sauer (2000), there are a large number of interesting theoretical ideas developed around the theme in the last years of the last century. The numerical schemes proposed are based on the Newton formulas. Recently in (Siam Rev. 61, 361–381 2019), R.D Neidinger has studied the multivariate polynomial interpolation problem using the techniques of Newton’s polynomial interpolation and the divided difference. In this work, we propose another approach to study the problem of the Lagrange multivariate polynomial interpolation in a particular case where the set of the interpolation nodes is a grid. Indeed, to solve this problem, we will use the Schur complement (Brezinski J. Comput. Appl. Math. 9, 369–376 1983; Brezinski Linear Algebra Appl. 111, 231–247 1988; Cottle Linear Algebra Appl. 8, 189–211 1974; Ouellette Linear Algebra Appl. 36, 187–295 1981; Schur J. Reine. Angew. Math. 147, 205–232 1917) and we will give a new algorithm for computing the interpolating polynomial which will be called the Recursive MultiVariate Polynomial Interpolation Algorithm: RMVPIA. A simplified version and some properties of this algorithm will be also studied and some examples will be given.

。拉格朗日或厄米单变量多项式插值的问题已经由最近一些研究（格斯克和洛佩兹-Carmona的J.约理论处理。34 361-374 1982; Messaoudi等NUMER算法学家。80，253-278 2019; Messaoudi和萨多克NUMER算法学家76，675-694 2017; Muhlbach NUMER数学31，97-110 1978）。多元多项式插值的研究是更加困难和方法是不太明显（格斯克和洛佩兹-Carmona的J.约理论。34，361-374 1982;格斯克和Sauer 2000;洛伦兹2000; Muhlbach NUMER数学31， 97–110 1978； Neidinger Siam修订版61，361–381 2019）。在加斯卡和索尔（Gasca and Sauer，2000）中，上个世纪的最后几年围绕这个主题发展了许多有趣的理论思想。提出的数值方案基于牛顿公式。最近，在（暹罗启61，361-381 2019），RD Neidinger研究了使用牛顿多项式插值的技术和分差多元多项式插值问题。在这项工作中，我们提出了另一种方法来研究在特定情况下内插节点集是网格的拉格朗日多元多项式内插问题。事实上，为了解决这个问题，我们将使用舒尔补（布热津斯基J. COMPUT应用数学。9，1983年369-376;布热津斯基线性代数申请111，231–247 1988；科特线性代数应用 8，189-211 1974; Ouellette线性代数应用 36，187-295 1981; Schur J. Reine。Angew。数学。147，205-232 1917），我们会给计算插值多项式将被称为递归多元多项式插值算法一种新的算法：RMVPIA。还将研究该算法的简化版本和某些属性，并给出一些示例。