Least-Change Secant Updates of Nonsquare Matrices
Samih K. Bourji, Homer F. Walker · SIAM Journal on Numerical Analysis · 1990
The notion of least-change secant updates is extended to apply to nonsquare matrices in a way appropriate for quasi-Newton methods used to solve systems of nonlinear equations that depend on parameters. Extensions of the widely used least-change secant updates for square matrices are given. A local convergence analysis for certain paradigm iterations is outlined as motivation for the use of these updates, and numerical experiments involving these iterations are discussed.