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Efficient inexact Newton-like methods with application to problems of the deformation theory of plasticity

Radim Blaheta, Roman Kohut (1993)

Applications of Mathematics

Newton-like methods are considered with inexact correction computed by some inner iterative method. Composite iterative methods of this type are applied to the solution of nonlinear systems arising from the solution of nonlinear elliptic boundary value problems. Two main quastions are studied in this paper: the convergence of the inexact Newton-like methods and the efficient control of accuracy in computation of the inexact correction. Numerical experiments show the efficiency of the suggested composite...

Epsilon-inflation with contractive interval functions

Günter Mayer (1998)

Applications of Mathematics

For contractive interval functions [ g ] we show that [ g ] ( [ x ] ϵ k 0 ) ⊆ ∫ ( [ x ] ϵ k 0 ) results from the iterative process [ x ] k + 1 : = [ g ] ( [ x ] ϵ k ) after finitely many iterations if one uses the epsilon-inflated vector [ x ] ϵ k as input for [ g ] instead of the original output vector [ x ] k . Applying Brouwer’s fixed point theorem, zeros of various mathematical problems can be verified in this way.

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