More process simulation in singular regions
Date of Original Version
The behavior of Newton-based equation-solving methods in regions containing saddle points is studied. It is shown that saddle points can cause Newton's method to settle into periodic or aperiodic orbits or diverge. To improve reliability and computational efficiency, a quadratic acceleration technique is used in the context of a complex domain trust region method together with approximate eigendecomposition in these and other singular regions. The quadratic acceleration technique gives rapid convergence to saddle points while the approximate eigenvalueeigenvector decomposition provides a path from any saddle point to a solution. A numerical example for a binary mixture with retrograde behavior is used to illustrate the key features of the algorithm. © 1999 Elsevier Science Ltd.
Computers and Chemical Engineering
Lucia, Angelo, and Delong Liu. "More process simulation in singular regions." Computers and Chemical Engineering 23, SUPPL. 1 (1999). doi:10.1016/S0098-1354(99)80090-8.