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Mathematics of Computation

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Efficient computer manipulation of tensor products with applications to multidimensional approximation

Authors: V. Pereyra and G. Scherer
Journal: Math. Comp. 27 (1973), 595-605
MSC: Primary 65F30; Secondary 65D05
MathSciNet review: 0395196
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Abstract: The objective of this paper is twofold: (a) To make it possible to perform matrix-vector operations in tensor product spaces, using only the factors ($n \cdot {p^2}$ words of information for $\otimes _{i = 1}^n{A_i},{A_i} \in \mathcal {L}({E^p},{E^p})$) instead of the tensor-product operators themselves (${({p^2})^n}$ words of information). (b) To produce efficient algorithms for solving systems of linear equations with coefficient matrices being tensor products of nonsingular matrices, with special application to the approximation of multidimensional linear functionals.

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Keywords: Computer manipulation of tensor products, multidimensional functional approximation, construction of finite elements, tensor product systems
Article copyright: © Copyright 1973 American Mathematical Society