Abstract

Charlie Van Loan: Approximation with Kronecker Products

The bridge between numerical linear algebra and numerical multilinear algebra is the Kronecker product.

Kron(B,C) is a block matrix whose (i,j) block is B(i,j)*C.

I will talk about three research problems that illustrate this point.

(a) How to approximate a Markov matrix A with the Kronecker product of two (smaller) Markov matrices B and C. (Completed Work)

(b) How to ``compress'' a 3D tensor A = {A(i,j,k)} using the Kronecker Product singular value decomposition. (Half-Baked Work)

(c) How to orchestrate a Fast Fourier Transform on unequally spaced data using an approximate matrix factorization of the underlying transform matrix. (Conjecture-level Work)