Preconditioning linearized equations (Q678117)

This note deals with the problem of numerically finding a root of a function \(f:X\to {\mathbb{R}}^n\) with some interval \(X \subset {\mathbb{R}}^n\). In particular, this note compares the following possibilities: (1) Usually, one first linearizes the equation and the preconditions of the resulting linear equation. (2) Alternatively, one can first precondition the original nonlinear equation. The author shows that the second possibility is better. In particular, it is claimed that the suggested procedure generally produces more rapid convergence. However, the computational effort is comparable.