Bounded homotopies to solve systems of sparse algebraic nonlinear equations

Computers and Chemical Engineering

Volumn 21, Issue 5, 1997, Pages 531-541

  Paloschi, Jorge R ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Bounded domains; Continuation methods; Homotopies; Sparse; Systems of nonlinear equations

Indexed keywords

ALGEBRA; BOUNDARY CONDITIONS; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; COMPUTER SIMULATION; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; ROBUSTNESS (CONTROL SYSTEMS);

CONTINUATION METHODS; HOMOTOPIES;

CHEMICAL EQUIPMENT;

EID: 0030652720     PISSN: 00981354     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0098-1354(96)00287-6     Document Type: Article

References (23)

1. Allgower E.L. and Georg K., Simplicial and continuation methods for approximating fixed points and solutions to systems of equations, SIAM Review, 22, (1980) 28-85
2. Allgower, E. L. and Georg, K., Numerical continuation methods - An introduction. Springer-Verlag (1990).
3. Allgower, E. L. and Georg, K., Continuation and path following. Acta Numerica, 1-64 (1993).
4. Broyden C.G., A class of methods for solving nonlinear simultaneous equations, Math. Comp., 19, (1965) 577-593
5. Curtiss A.R., Powell M.J.D. and Reid J.K., On the estimation of sparse Jacobian matrices, J. Inst. Math. Applic., 13, (1974) 117-119
6. Dennis, J. D. and Schnabel, R. B., Numerical methods for unconstrained optimization and nonlinear equations. Prentice Hall, Englewood Cliffs, New Jersey (1983).
7. Duff I.S., Algorithm 575. Permutations for a zero free diagonal, ACM TOMS, 7, (1981) 387
8. Edwards, D. W., Robust decomposition techniques for process design and simulation. Ph.D. thesis, University of London, Imperial College (1982).
9. Hiebert K.L., An evaluation of mathematical software that solves systems of nonlinear equations, ACM TOMS, 8, (1982) 5-20
10. Kubicek M., Algorithm 502: Dependence of Solution of Nonlinear Systems on a Parameter, ACM TOMS, 2, (1976) 98-107
11. More, J. J., A collection of nonlinear model problems. In Computational solution of nonlinear systems of equations (Allgower E. L. and Georg, K., Eds.). American Mathematical Society, 723-761 (1990).
12. Ortega, J. M. and Rheinboldt, W. C., Iterative solution of nonlinear equations in several variables. Academic Press, New York (1970).
13. Paloschi J.R., Bounded homotopies to solve systems of algebraic nonlinear equations, Comput. chem. Engng, 19, (1995) 1243-1254
14. Paloschi, J. R., Using Sparse bounded homotopies in steady state simulation packages. Comp. Chem. Engng 20, 5285-5290 (1996).
15. Rheinboldt W. and Burkardt J., A locally parameterized continuation process, ACM Transactions on Mathematical Software, 9, (1983) 215-235
16. Schubert L.K., Modification of a Quasi-Newton method for nonlinear equations with a sparse Jacobian. Math. Comp., 24, (1970) 27-30
17. Seader, J. D., Recent developments in methods for finding all solutions to general systems of nonlinear equations. In Foundations of Computer Aided Process Design (J. J. Siirola, I. E. Grossmann and G. Stephanopoulos, Eds.), pp. 181-207. Elsevier, New York (1990).
18. Seader J.D., Kuno M., Lin W.J., Johnson S.A., Unsworth K. and Wiskin J.W., Mapped continuation methods for computing all solutions to general systems of nonlinear equations, Comput. Chem. Engng., 14, (1990) 71-85
19. Shacham, M., Recent developments in solution techniques for systems of nonlinear equations. In 2nd. FOCAPD Conference, Snowmass, Colorado, June 1983, pp. 891-923 (1983).
20. Shacham M., Comparing software for the solution of systems of nonlinear algebraic equations arising in chemical engineering, Comput. Chem. Engrg., 9, (1985) 103-112
21. Toint P.L., On sparse and symmetric matrix updating subject to a linear equation, Math. Comp., 31, (1977) 954-961
22. Watson L.T., Billups S.C. and Morgan A.P., ALGORITHM 652: HOMPACK: A suite of codes for globally convergent homotopy algorithms, ACM TOMS, 13, (1987) 281
23. Wayburn T.L. and Seader J.D., Homotopy continuation methods for computer aided process design, Comput. chem. Engng, 11, (1987) 7-25