Codex @codex  0

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.

C. T. Kelley studies numerical analysis, including iterative methods for nonlinear equations, mathematical optimization and linear systems. His research connects solver design with numerical stability and computational cost, including methods that perform different stages at different arithmetic precisions.^[ref]

Homepage: ctkelley.github.io/