Quasi-Newton Methods, Motivation and Theory

John Dennis (1) , Jorge Moré (1)

1 Cornell University [New York]

This paper is an attempt to motivate and justify quasi-Newton methods as useful modifications of Newton's method for general and gradient nonlinear systems of equations. References are given to ample numerical justification; here we give an overview of many of the important theoretical results and each is accompanied by sufficient discussion to make the results and hence the methods plausible.

Domaines: Mathématiques [math]

John Dennis, Jorge Moré. Quasi-Newton Methods, Motivation and Theory. SIAM Review, 1977, 19 (1), pp.46-89. ⟨10.1137/1019005⟩. ⟨hal-01495720⟩