Charles Van Loan
PhD Michigan, 1973
With CS undergraduate D. Bernstein, I continued to work on an
inverse problem that arises in pharmakinetics. We had to compute a transition matrix given
snapshots of the solution to a certain system of differential equations. The matrix turns
out to be a minimizer of a nonlinear least squares problem whose solution was made very
efficient by using a generalization of the Sherman-Morrison update formula developed by
us. Using this result, we were able to refine our earlier method so that it computes an
exact Jacobian an order of magnitude faster than before.
I continue to work on various applications of the
Kronecker product (KP). I generalized some of J. Nagy's work on preconditioners for block
Toeplitz linear systems using KP approximation ideas developed earlier.
Director: Undergraduate Studies, Computer Science
Chair: Ad Hoc Committee on Biology, College of
Chair: Academic Standards, Petitions and Actions
Committee, College of Engineering
Core Curriculum Governing Board, College of
Co-op Advisory Board, College of Engineering
Organizing Committee: Householder Conference;
Householder Prize Committee.
Applications of the Kronecker product. The Western
Michigan Conf. Matrix Methods, Kalamazoo, Michigan, Oct. 1997.
Applications of the Kronecker product. SIAM Conf.
Linear Algebra, Snowbird, Utah, Nov. 1997.