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,

$Ax = \lambda Bx$
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.