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.

Ilse Ipsen works in numerical linear algebra, randomized algorithms, the theory of matrices and scientific computing. Her research also connects numerical methods with nonlinear problems, parameter estimation and statistics. These topics concern both efficient computation and how approximation errors or perturbations affect the reliability of a calculated result.^[ref]