Preconditioned sequential and parallel conjugate gradient algorithms for homotopy curve tracking

There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Variants of the conjugate gradient algorithm along with different preconditioners are implemented in the context of homotopy curve tracking and compared with Craig's preconditioned conjugate gradient method used in HOMPACK. In addition, a parallel version of Craig's method with incomplete LU factorization preconditioning is implemented on a shared memory parallel computer with various levels and degrees of parallelism (e.g., linear algebra, function and Jacobian matrix evaluation, etc.). An in-depth study is presented for each of these levels with respect to the speedup in execution time obtained with the parallelism, the time spent implementing the parallel code and the extra memory allocated by the parallel algorithm.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Computer Science and Applications

Department dc:contributor.department

Computer Science and Applications

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1990

Author dc:creator

• Irani, Kashmira M.

Chair dc:contributor.committeechair

• Watson, Layne T.

Committee members dc:contributor.committeemember

• Ribbens, Calvin J.
• Herdman, Terry L.

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

etd-04082009-040342

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/41971