POLYNOMIAL INTERPOLATION IN NONDIVISION ALGEBRAS∗
POLYNOMIAL INTERPOLATION IN NONDIVISION ALGEBRAS∗
复制标题
不可除代数中的多项式插值*
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
G. Opfer
中科院分区：
文献类型：
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作者：
G. Opfer
给出了不可除代数中两类插值多项式的算法。一个是基于范德蒙矩阵，另一个是接近牛顿插值方案。例子取自R4-代数。在Vandermonde情形下，给出了交换代数存在插值多项式的充分必要条件。对于非交换代数，提出了一个猜想。这个猜想对于等距节点是正确的。证明了插值多项式的牛顿形式存在当且仅当所有节点差可逆。给出了几个数值算例。
Algorithms for two types of interpolation polynomials in nondivision algebras are presented. One is based on the Vandermonde matrix, and the other is close to the Newton interpolation scheme. Examples are taken from R4-algebras. In the Vandermonde case, necessary and sufficient conditions for the existence of interpolation polynomials are given for commutative algebras. For noncommutative algebras, a conjecture is proposed. This conjecture is true for equidistant nodes. It is shown that the Newton form of the interpolation polynomial exists if and only if all node differences are invertible. Several numerical examples are presented.