Condition Estimates for Pseudo-Arclength Continuation by K. I. Dickson and others (2007, 10.1137/060654384)

By K. I. Dickson, C. T. Kelley, Ilse Ipsen, Yannis G. Kevrekidis.

Publisher: Society for Industrial and Applied Mathematics.

Published in SIAM Journal on Numerical Analysis, volume 45, number 1, pp. 263–276.

Online text: ipsen.math.ncsu.edu/ps/sinum65438.pdf

Cited passages: §2.1, Corollary 2.1, printed pp. 264–265: Lipschitz continuously differentiable map, nonsingular state Jacobian, and a sufficiently small parameter increment; §2.2, Definition 2.2, printed p. 265: one-dimensional kernel of the state Jacobian and parameter derivative outside its range; §2.2, equations (2.2)–(2.5), printed pp. 265–266: unit tangent and hyperplane normalization; Corollary 2.3 gives local Newton convergence for sufficiently small steps.