The best parameter for extension of a solution. (English. Russian original) Zbl 0851.65027

Shalashilin, V. I.; Kuznetsov, E. B.

Russ. Acad. Sci., Dokl., Math. 49, No. 1, 170-173 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 334, No. 5, 566-568 (1994).

For tracing the solution curve of a system of \(n\) nonlinear equations in \(n+ 1\) unknowns one has to choose an appropriate parametrization. In this paper, it is shown that the arclength parametrization leads to the best conditioning of an augmented Jacobian of the system, where conditioning of a matrix is measured by the determinant divided by the product of the Euclidean norm of the rows.

Reviewer: W.Zulehner (Linz)

MSC:

65H10	Numerical computation of solutions to systems of equations
65F35	Numerical computation of matrix norms, conditioning, scaling
65H20	Global methods, including homotopy approaches to the numerical solution of nonlinear equations

Keywords:

implicitly defined curves; path following methods; arclength parametrization; conditioning; augmented Jacobian