In this manuscript, we present a common tensor framework which can be used to generalize one-dimensional numerical tasks to arbitrary dimension $d$ by means of tensor product formulas. This is useful, for example, in the context of multivariate interpolation, multidimensional function approximation using pseudospectral expansions and solution of stiff differential equations on tensor product domains. The key point to obtain an efficient-to-implement BLAS formulation consists in the suitable usage of the $\mu$-mode product (also known as tensor-matrix product or mode- $n$ product) and related operations, such as the Tucker operator. Their MathWorks MATLAB/GNU Octave implementations are discussed in the paper, and collected in the package KronPACK. We present numerical results on experiments up to dimension six from different fields of numerical analysis, which show the effectiveness of the approach.

翻译：在本手稿中,我们提出了一个共同的强力框架,可以用高压产品公式将一维数字任务概括为任意的维度美元,例如,在多变量内插、多功能近似、使用假光谱扩展和在高压产品域的硬性差异方程解决方案的背景下,这是有用的。获得高效实施BLAS配方的关键点是适当使用$mu$-mode产品(又称Exron-matrix产品或方式-美元产品)和相关操作,例如塔克操作员。他们的数学工作MATLAB/GNU Octave的落实情况在文件中讨论,并在整套KronPACK中收集。我们介绍了从数字分析的不同领域到第六层面的实验结果,这些实验显示了方法的有效性。