Homotopy continuation methods for computer-aided process design

1987 ◽  
Vol 11 (1) ◽  
pp. 7-25 ◽  
Author(s):  
T.L. Wayburn ◽  
J.D. Seader
Keyword(s):  
Process Design ◽  
Continuation Methods ◽  
Homotopy Continuation ◽  
Computer Aided ◽  
Homotopy Continuation Methods

Numerical solution of multivariate polynomial systems by homotopy continuation methods

Acta Numerica ◽  
1997 ◽  
Vol 6 ◽  
pp. 399-436 ◽  
Author(s):  
T. Y. Li
Keyword(s):  
Power Flow ◽  
Polynomial Systems ◽  
Continuation Methods ◽  
Homotopy Continuation ◽  
Multivariate Polynomial ◽  
Science And Engineering ◽  
Flow Problems ◽  
Homotopy Continuation Methods ◽  
Buchberger Algorithm ◽  
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Let P(x) = 0 be a system of n polynomial equations in n unknowns. Denoting P = (p1,…, pn), we want to find all isolated solutions offor x = (x1,…,xn). This problem is very common in many fields of science and engineering, such as formula construction, geometric intersection problems, inverse kinematics, power flow problems with PQ-specified bases, computation of equilibrium states, etc. Elimination theory-based methods, most notably the Buchberger algorithm (Buchberger 1985) for constructing Gröbner bases, are the classical approach to solving (1.1), but their reliance on symbolic manipulation makes those methods seem somewhat unsuitable for all but small problems.

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