# Eecient Solution of the Jacobian System in Newton's Method Close to a Root

@inproceedings{Drexler1997EecientSO, title={Eecient Solution of the Jacobian System in Newton's Method Close to a Root}, author={RootMichael Drexler and Gene H. Golub}, year={1997} }

- Published 1997

Newton's Method constitutes a nested iteration scheme with the Newton step as the outer iteration and a linear solver of the Jacobian system as the inner iteration. We examine the interaction between these two schemes and derive solution techniques for the linear system from the properties of the outer Newton iteration. Contrary to inexact Newton methods, our techniques do not rely on relaxed tolerances for an iterative linear solve, but rather on computational speedup achieved by exploiting… CONTINUE READING

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## Choosing the Forcing Terms in an Inexact Newton Method

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## On Algorithms for Solving f(x) = 0, Communications on

View 1 Excerpt

## Quasi-Newton Methods, Motivation and Theory

View 1 Excerpt

## Methods for Modifying Matrix Factorizations

View 1 Excerpt

## The Di erentiation of Pseudo-Inverses and Non-linear Least Squares Problems Whose Variables Separate

View 1 Excerpt

## Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables

View 1 Excerpt