Optimal homotopy methods for solving nonlinear systems. I: Nonsingular homotopy paths. (English) Zbl 0797.65045
The authors prove that in solving systems of nonlinear equations, a homotopy with a given structure has a distance monotone path under some regular conditions. The so-called local straighten-up method and global straighten-up method, as well as an adaptive step-size control strategy, are developed to approximate the optimal homotopy.
Reviewer: Wang Zeke (Guangzhou)
MSC:
| 65H10 | Numerical computation of solutions to systems of equations |
| 65H20 | Global methods, including homotopy approaches to the numerical solution of nonlinear equations |
Keywords:
distance monotone path; systems of nonlinear equations; straighten-up method; adaptive step-size control strategy; optimal homotopyReferences:
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