On minimal subspaces in tensor representations
There has recently been an increased interest in numerical methods which make use of tensors. Two families of applications using tensor decompositions are in the extraction and in the compression of information from complex data. Tensor product approximations are also being increasingly used in numerical analysis for the solution of problems defined in high-dimensional tensor spaces, such as certain PDEs. The authors introduce the concept of a minimal subspace of an algebraic tensor and describe a characterization. Minimal subspaces are defined and characterized for Banach tensor spaces and are used to prove the existence of a best approximation for any element in a Banach tensor space with a norm stronger than the injective norm. Examples using topological tensor products of standard Sobolev spaces are given.
scientific article; zbMATH DE number 6121322
scientific article