Craig Lucas
I was a research student here at the School of Mathematics from 2001 to 2004. I then worked in the High Performance Computing team in Research Computing, but am now at the Numerical Algorithms Group (NAG).
I am very pleased to be still associated with the NA Group at
Manchester. Firstly working with
Nick Higham and
Rüdiger Borsdorf
as Rüdiger's Industrial
Supervisor. And secondly, with Nick,
Françoise Tisseur and
Edvin Deadman on the Matrix Functions KTP project.
PhD and before
PhD
My research area was Numerical Linear Algebra under the supervision of Nick Higham. My thesis is entitled Algorithms for Cholesky and QR Factorizations, and the Semidefinite Generalized Eigenvalue Problem. It covers these problems:- Level 2 and Level 3 BLAS LAPACK code for the pivoted Cholesky
factorization of a symmetric positive semidefinite
matrix.
Cholesky page here.
- Some Updating Matrix Factorizations problems, such as
if we know a QR factorization
then we wish to compute
efficiently, where is with blocks of rows or columns added or deleted.Updating page here.
- The Symmetric
Semidefinite Generalized Eigenvalue Problem,
whereand are symmetric and one is positive semidefinite.
MSc
My MSc thesis was Computing Nearest Covariance and Correlation Matrices, and files to download.BSc
My BSc project was The Numerical Investigation of a Model for the Body Dynamics of a Swimming Lamprey.Papers
- Updating the QR factorization and the least squares problem, with Sven Hammarling, MIMS EPrint 2008.111. November, 2008.
- LAPACK-Style Codes for Pivoted Cholesky and QR Updating,, with Nick Higham and Sven Hammarling, PARA06, Umeå, Sweden, June 18-21, 2006.
- Symmetric Pivoting in ScaLAPACK, Cray User Group, Lugano, Switzerland. May 8-11, 2006.
- LAPACK-Style Codes for Level 2 and 3 Pivoted Cholesky Factorizations, Technical Report, Manchester Centre for Computational Mathematics, February, 2004. Also available from LAPACK in PostScript as Working Note 161.