Optimal parametrization in numerical construction of curve. (English) Zbl 1269.65049
Summary: The application of the optimal parametric continuation method to constructing a solution set curve for a system of nonlinear algebraic or transcendental equations depending on a parameter is considered. There are discussed two approaches to solving this problem - the use of iterative methods and reduction to an initial value problem for a system of ordinary differential equations. The algorithm suggested in this paper can also be used for finding an appropriate initial approximation when solving a system of nonlinear algebraic or transcendental equations not depending on a parameter by an iterative method.
MSC:
| 65H20 | Global methods, including homotopy approaches to the numerical solution of nonlinear equations |
Keywords:
curve construction; optimal parametrization; iterative methods; nonlinear algebraic; transcendental equationsReferences:
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