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

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


Publications citing this paper.


Publications referenced by this paper.
Showing 1-8 of 8 references

Numerical methods for unconstrained optimization and nonlinear equations

Prentice Hall series in computational mathematics • 1983
View 2 Excerpts

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

M. W. Hirsch, S. Smale
Pure and Applied Mathematics, Vol • 1979
View 1 Excerpt

Quasi-Newton Methods, Motivation and Theory

J. E. Dennis, J. J. Mor e
SIAM Review, • 1977
View 1 Excerpt

Methods for Modifying Matrix Factorizations

P. E. Gill, G. H. Golub, W. Murray, M. A. Saunders
Mathematics of Computation, • 1974
View 1 Excerpt

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

G. H. Golub, V. Pereyra
SIAM Journal on Numerical Analysis, • 1973
View 1 Excerpt

Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables

W.C.J.M. Ortega
View 1 Excerpt

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