Time-varying Computational Networks: Realization, Orthogonal Embedding and Structural Factorization
A. van Veen, Patrick M. Dewilde · Research Repository (Delft University of Technology) · 1992
Many computational schemes in linear algebra can be studied from the point of view of (discrete) time-varying linear systems theory.For example, the operation 'multiplication of a vector by an upper triangular matrix' can be represented by a computational scheme (or model) that acts on the entries of the vector sequentially.The number of intermediate quantities ('states') that are needed in the computations is a measure of the complexity of the model.If the matrix is large but its complexity is low, then not only multiplication, but also other operations such as inversion and factorization, can be carried out efficiently using the model rather than the original matrix.In the present paper we discuss a number of techniques in time-varying system theory that can be used to capture a given matrix into such a computational network.