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

A $\mu$-mode BLAS approach for multidimensional tensor-structured problems