Charles Van Loan
Professor and Chair
I continue to work in the computational multilinear algebra area. This includes factorization approaches to various fast transforms, Kronecker product preconditioners, and Kronecker-constrained least squares problems.
This past year Adam Florence and I developed a new way to look at the fast Gauss transform (FGT) of Greengard and Strain. Like all fast transforms, the trick is to exploit the structure of the underlying transform matrix. Behind the FGT is an approximate sparse matrix factorization. We are able to improve the efficiency of the FGT by improving the error bounds associated with the approximate factorization and by identifying the Kronecker product structure of the factor matrices.
Other research results concern the approximation of a given vector by a k-fold “Kronecker power” of another vector and the solution of the total least squares problem when the data matrix is a Kronecker product.
Chair: Department of Computer Science.
Director of Undergraduate Studies: Department of Computer Science.
Member: Core Curriculum Governing Board (Engineering); Computing Policy Commitee (Engineering); College Scholar Advisory Committee (Arts and Sciences).
Reader: Freshman Admissions (Arts and Sciences).
“Rational Matrix Functions and Rank-1 Updates.” SIAM Journal on Matrix Analysis and Applications 22 (2000), 145-154 (with D. S. Bernstein).
The Ubiquitous Kronecker Product. New York University, New York, NY, February 2000.