Computer Science Technical Reports
CS at VT

Probability-one Homotopies in Computational Science

Watson, Layne T. (2000) Probability-one Homotopies in Computational Science. Technical Report TR-00-03, Computer Science, Virginia Tech.

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Probability-one homotopy algorithms are a class of methods for solving nonlinear systems of equations that,under mild assumptions,are globally convergent for a wide range of problems in science and engineering.Convergence theory, robust numerical algorithms,and production quality mathematical software exist for general nonlinear systems of equations, and special cases suc as Brouwer fixed point problems,polynomial systems,and nonlinear constrained optimization.Using a sample of challenging scientific problems as motivation,some pertinent homotopy theory and algorithms are presented. The problems considered are analog circuit simulation (for nonlinear systems),reconfigurable space trusses (for polynomial systems),and fuel-optimal orbital rendezvous (for nonlinear constrained optimization).The mathematical software packages HOMPACK90 and POLSYS_PLP are also briefly described.

Item Type:Departmental Technical Report
Keywords:Globally convergent homotopy method;Mathematical software;Nonlinear equations;Polynomial systems
Subjects:Computer Science > Parallel Computation
ID Code:559
Deposited By:User, Eprints
Deposited On:22 May 2002