Lorenzetti, D.
(2017),
Regulating Newton-Raphson's Method by Unconstrained Minimization of a Weighted Sum of Squared Residuals, Siam Journal on Scientific Computing
(Accessed July 19, 2024)
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Regulating Newton-Raphson's Method by Unconstrained Minimization of a Weighted Sum of Squared Residuals
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Abstract
To control the Newton-Raphson solution of a nonlinear algebraic system, a descent method forces each step to reduce some norm of the residual errors. This prevents divergence, but risks stagnation in flat regions of the norm. Employing a family of cost functions -- here a weighted sum of squaredresiduals -- allows a solver, in principle, to avoid all minima except at the desired solution. Geometric arguments suggest several rules for choosing weights, and numerical experiments show these improve the global convergence of a representative method, provided the weights incorporate sufficient information from the residual models at each iteration. The technique extends to otherminimization based equation solvers, either directly, or through its interpretation as a means of automatically rescaling the residuals.Citation
Siam Journal on Scientific Computing
Pub Type
Journals
Keywords
indefinite dogleg, Newton-Raphson, nonlinear system, scaling, trust region
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Created February 19, 2017