Research
My research interests are in designing efficient algorithms and software for numerical linear algebra problems. I currently concentrate on problems involving sparse matrices and banded matrices. Specifically, I have worked on direct methods for sparse singular value decompostion, band reduction for band singular value and eigen value decomposition and ordering techniques for sparse Cholesky and LU factorizations.
Publications
- Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky factorization and Update / Downdate, Y. Chen, T. A. Davis, W. W. Hager, and S. Rajamanickam, ACM Transactions on Mathematical Software, 2008, Volume 35, Number 3.(Citations)
- Blocked Band Reduction of Symmetric and Unsymmetric Matrices, T. A. Davis and S. Rajamanickam, To be submitted to ACM Transactions on Mathematical Software.Manuscript available.
- Algorithm 8xx: PIRO BAND, Pipelined Plane rotations for Band Reduction, T. A. Davis and S. Rajamanickam, To be submitted to ACM Transactions on Mathematical Software. Manuscript available.
- Blocked Bidiagonal Reduction of Sparse Matrices and Sparse Singular Value Decomposition, T. A. Davis and S. Rajamanickam, In preparation.
Software
CCOLAMD generates constraint preserving ordering that reduces fill-in and requires fewer floating point operations in sparse Cholesky and sparse LU factorizations. It is based on COLAMD. CCOLAMD is part of CHOLMOD. Download or Browse CCOLAMD code.
PIRO_BAND reduces symmetric/unsymmetric band matrices to tridiagonal/bidiagonal form. PIRO_BAND supports double and single precision arithmetic for real and complex matrices in architectures with 32-bit and 64-bit integers. PIRO_BAND can also compute the SVD for a band matrix. Browse PIRO_BAND code (beta) or Download PIRO_BAND (beta).
PIRO_SKY finds the singular value decomposition of sparse matrices. PIRO_SKY uses a sparse QR factorization and sparse tridigonalization of the R from the QR factorization to compute the SVD of the sparse matrix. PIRO_SKY will be released in Fall 2009. Send me an e-mail if you would like to see the current version of the code.
Past work
In the past, I was part of the application server development team at Sun Microsystems. My contributions were mostly in the software load balancing module and servlet container modules. I was also part of the development team for print spoolers in Tandem computers/NonStop servers, a Fault Tolerant system from the 70's. It is part of the HP NonStop computing servers now.