zbMATH — the first resource for mathematics

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

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