Project Supervisor: Prof. John Cremona, Mathematics
Title: “Parallelization of simultaneous eigenvector computations for large sparse integer matrices”
Abstract
Given a sequence of large sparse square commuting matrices with integer entries
T1,T2,T3,..., and a short list of possible integer eigenvalues for each one, it is desired to find a basis for the corresponding simultaneous eigenspace. An implementation (in C++) exists to do this using sparse linear algebra and a recursive strategy. The project would be to adapt this code to work in parallel, so that each possible eigenvalue of T1 could be handled simultaneously instead of one at a time, and similarly for the later operators. The mathematical background required would only consist of basic linear algebra and modular arithmetic. The intended application for this code is to extend the elliptic curve database at http://www.warwick.ac.uk/staff/J.E.Cremona/ftp/data/ but no knowledge of elliptic curves is necessary. Knowledge of programming in C and/or
C++ is essential.
John Cremona