1998 - 1999 CS Annual Report                                                                  Faculty
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Charles Van Loan


PhD Michigan, 1973

During the past year I have started to systematically research what I would call "computational multilinear algebra." This
includes factorization approaches to various fast transforms, Kronecker product preconditioners, and Kronecker- constrained least square problems. 

With respect to the last, Adam Florence and I have developed a Gauss-Newton penalty function method that 

seems pretty successful for the problem of minimizing the 2-norm of A*kron(x,y) - b. 

I am supervising two undergraduate research projects with CS majors. Ronnie Choy and I have developed a new implementation of the block Aasen method that can be used to solve symmetric indefinite linear systems. This method is competitive with the diagonal pivoting method that is part of LAPACK. With Lisa Fishman I started the Java Flag project. The idea is to write the "shortest"
possible applet that can generate all the national flags. 

I completed the second edition of my undergraduate scientific computing text. The new edition is consistent with Matlab version 5 and contains new material on graphics, trigonometric interpolation, structures, and cell arrays. 

Professional Activities  

  • Member: Householder Conference Organizing Committee 

  • Member: Householder Prize Committee

  • Matrix functions and rank-1 updates. Householder Conference, Whistler, British Columbia, June 1999. 
  • Introduction to Scientific Computing - A Matrix/Vector Approach Using Matlab (2nd Edition). Prentice Hall, (1999).  
  • GEMM-based level 3 BLAS: high performance model implementations and performance evaluation benchmark. ACM Transactions in Mathematical Software 24 (1998), 268-302. 
  • Algorithm 784: GEMM-based  level 3 BLAS: portability and optimization issues. ACM
    Transactions in Mathematical Software
    24 (1998), 303-316.