Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms

By Peter Deuflhard. 2011

798 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/d4480a77ffa24f6541ccf6e0fa3d03623d15609d

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Citations in the corpus

Adaptively Localized Continuation-Newton Method—Nonlinear Solvers That Converge All the Time (2010, methodology): “Using this property, a computational estimate of a Kantorovich condition on the Jacobian-matrix norm can be used to estimate whether the point in question is a good point to start a Newton iteration [see, for example, Deuflhard (2004) and Ortega and Rheinboldt (1970)].”
ON THE NEWTON–KANTOROVICH THEOREM (2012, background): “Interesting complements and in-depth treatments are found in Rheinboldt [11], Gragg and Tapia [6], Deuflhard [4], Dedieu [2], among others (this brief list is by no means intended to be exhaustive).”
Globally Convergent Newton Methods for Ill-conditioned Generalized Self-concordant Losses (2019, methodology): “In this paper, more generally we consider any technique to compute ∆̃λ(xt) that provides a relative approximation [16] of ∆λ(xt) defined as follows.”
Inverse problems: A Bayesian perspective (2010, methodology): “Yet another example may be found in the study of Newton methods: conceptual application of this algorithm on function space, before discretization, can yield considerable insight when applying it as an iterative method for boundary value problems in nonlinear differential equations (Deuflhard 2004).”
How much H and He is ‘hidden’ in SNe Ib/c? – I. Low-mass objects (2012, methodology): “When the accuracy estimator of NLEQ2 indicates convergence to 0.01%, we accept the solution.”
Optimal power flow: a bibliographic survey I (2012, methodology): “Inequality Constraints Constraint References Active/reactive power generation limits Gan et al. (2000); Chattopadhyay and Gan (2001) Demand constraints Momoh (1989) Bus voltage limits Dommel and Tinney (1968); Gan et al.”