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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.

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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.

University Activities

  • Director: Undergraduate Studies, Computer Science

  • Chair: Ad Hoc Committee on Biology, College of Engineering

  • Chair: Academic Standards, Petitions and Actions Committee, College of Engineering

  • Core Curriculum Governing Board, College of Engineering

  • Co-op Advisory Board, College of Engineering

Professional Activities

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.