Using Taylor-mode automatic differentiation, the authors implement scalable Halley's method for nonlinear systems and report speedups over Newton's method on dense, sparse, and ODE-internal solves.
Albeanu , On the generalized halley method for solving nonlinear equations , ROMAI J, 4 (2008), pp
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Scalable higher-order nonlinear solvers via higher-order automatic differentiation
Using Taylor-mode automatic differentiation, the authors implement scalable Halley's method for nonlinear systems and report speedups over Newton's method on dense, sparse, and ODE-internal solves.