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On the convergence of inexact Newton methods
, 2011
"... The inexact Newton method is widely used to solve systems of nonlinear equations. It is wellknown that forcing terms should be chosen relatively large at the start of the process, and be made smaller during the iteration process. This paper explores the mechanics behind this behavior theoretically ..."
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The inexact Newton method is widely used to solve systems of nonlinear equations. It is wellknown that forcing terms should be chosen relatively large at the start of the process, and be made smaller during the iteration process. This paper explores the mechanics behind this behavior
GLOBALLY CONVERGENT INEXACT NEWTON METHODS*
"... Abstract. Inexact Newton methods for finding a zero of F 1 1 are variations of Newton’s method in which each step only approximately satisfies the linear Newton equation but still reduces the norm of the local linear model of F. Here, inexact Newton methods are formulated that incorporate features d ..."
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Abstract. Inexact Newton methods for finding a zero of F 1 1 are variations of Newton’s method in which each step only approximately satisfies the linear Newton equation but still reduces the norm of the local linear model of F. Here, inexact Newton methods are formulated that incorporate features
An Inexact Newton Method for Systems . . .
 APPL. MATH. LETTERS
, 1996
"... In this paper we introduce an efficient and robust technique for approximating the Jacobian matrix for a nonlinear system of algebraic equations which arises from the finite element discretization of a system of nonlinear partial differential equations. It is demonstrated that when an iterative solv ..."
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solver, such as preconditioned GMRES, is used to solve the linear systems of equations that result from the application of Newton's method this approach is generally more efficient than using matrixfree techniques: the price paid being the extra memory requirement for storing the sparse Jacobian
A Nonmonotone Inexact Newton Method
 Optim. Methods Softw
, 2005
"... In this paper we describe a variant of the Inexact Newton method for solving nonlinear systems of equations. We define a nonmonotone Inexact Newton step and a nonmonotone backtracking strategy. For this nonmonotone Inexact Newton scheme we present the convergence theorems. Finally, we show how we ca ..."
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Cited by 3 (2 self)
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In this paper we describe a variant of the Inexact Newton method for solving nonlinear systems of equations. We define a nonmonotone Inexact Newton step and a nonmonotone backtracking strategy. For this nonmonotone Inexact Newton scheme we present the convergence theorems. Finally, we show how we
Inexact Newton Methods for Singular Problems
"... this paper we describe the effects of an inexact implementation of Newton's method on the behavior of the iteration for certain nonlinear equations in Banach space for which the Fr'echet derivative is singular at the solution. We give a termination criterion for the inner iteration that pr ..."
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Cited by 1 (0 self)
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this paper we describe the effects of an inexact implementation of Newton's method on the behavior of the iteration for certain nonlinear equations in Banach space for which the Fr'echet derivative is singular at the solution. We give a termination criterion for the inner iteration
Choosing the Forcing Terms in an Inexact Newton Method
 SIAM J. SCI. COMPUT
, 1994
"... An inexact Newton method is a generalization of Newton's method for solving F(x) = 0, F:/ /, in which, at the kth iteration, the step sk from the current approximate solution xk is required to satisfy a condition ]lF(x) + F'(x)s]l _< /]lF(xk)]l for a "forcing term" / [0,1). I ..."
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Cited by 161 (6 self)
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An inexact Newton method is a generalization of Newton's method for solving F(x) = 0, F:/ /, in which, at the kth iteration, the step sk from the current approximate solution xk is required to satisfy a condition ]lF(x) + F'(x)s]l _< /]lF(xk)]l for a "forcing term" / [0
Inexact Newton Methods for Solving Nonsmooth Equations
 Journal of Computational and Applied Mathematics
, 1999
"... This paper investigates inexact Newton methods for solving systems of nonsmooth equations. We define two inexact Newton methods for locally Lipschitz functions and we prove local (linear and superlinear) convergence results under the assumptions of semismoothness and BDregularity at the solution. W ..."
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Cited by 30 (9 self)
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This paper investigates inexact Newton methods for solving systems of nonsmooth equations. We define two inexact Newton methods for locally Lipschitz functions and we prove local (linear and superlinear) convergence results under the assumptions of semismoothness and BDregularity at the solution
Convergence Behaviour of Inexact Newton Methods
 Mathematics of Computation
, 1999
"... Abstract. In this paper we investigate local convergence properties of inexact Newton and Newtonlike methods for systems of nonlinear equations. Processes with modified relative residual control are considered, and new sufficient conditions for linear convergence in an arbitrary vector norm are pro ..."
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Cited by 22 (1 self)
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Abstract. In this paper we investigate local convergence properties of inexact Newton and Newtonlike methods for systems of nonlinear equations. Processes with modified relative residual control are considered, and new sufficient conditions for linear convergence in an arbitrary vector norm
Convergence of inexact Newton methods for generalized equations
 Math. Programming B
"... Abstract. For solving the generalized equation f(x) + F (x) ∋ 0, where f is a smooth function and F is a setvalued mapping acting between Banach spaces, we study the inexact Newton method described by (f(xk) + Df(xk)(xk+1 − xk) + F (xk+1)) ∩ Rk(xk, xk+1) = ∅, where Df is the derivative of f and ..."
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Cited by 5 (1 self)
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Abstract. For solving the generalized equation f(x) + F (x) ∋ 0, where f is a smooth function and F is a setvalued mapping acting between Banach spaces, we study the inexact Newton method described by (f(xk) + Df(xk)(xk+1 − xk) + F (xk+1)) ∩ Rk(xk, xk+1) = ∅, where Df is the derivative of f
A nonmonotone semismooth inexact Newton method
"... In this work we propose a variant of the inexact Newton method for the solution of semismooth nonlinear systems of equations. We introduce a nonmonotone scheme, which couples the inexact features with the nonmonotone strategies. For the nonmonotone scheme, we present the convergence theorems. Finall ..."
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In this work we propose a variant of the inexact Newton method for the solution of semismooth nonlinear systems of equations. We introduce a nonmonotone scheme, which couples the inexact features with the nonmonotone strategies. For the nonmonotone scheme, we present the convergence theorems
Results 1  10
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