Efficient computer manipulation of tensor products with applications to multidimensional approximation

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 ⋅ p 2 n · {p^2} words of information for ⊗ i = 1 n A i , A i ∈ L ( E p , E p ) ⊗ i = 1^n{A_i},{A_i} ∈ L({E^p},{E^p}) ) instead of the tensor-product operators themselves ( ( p 2 ) n {({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.