Newton’s method and some complexity aspects of the zero-finding problem. (English) Zbl 0978.65048

DeVore, Ronald A. (ed.) et al., Foundations of computational mathematics. Conference, Oxford, GB, July 18-28, 1999. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 284, 45-67 (2001).
Summary: Newton’s iteration is a classical numerical method to find a zero of a system of nonlinear equations. In this paper we discuss recent advances in this subject: homogeneous and multihomogeneous systems, overdetermined and underdetermined systems are considered. We also discuss some complexity aspects of continuation methods using Newton’s method.
For the entire collection see [Zbl 0962.00005].


65J15 Numerical solutions to equations with nonlinear operators
47J25 Iterative procedures involving nonlinear operators
65Y20 Complexity and performance of numerical algorithms