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Analysis and modification of Newton's method at singularities

Griewank, Andreas Otto


For systems of nonlinear equations f=0 with singular Jacobian Vf(x*) at some solution x* E F-1(0) the behaviour of Newton's method is analysed. Under certain regularity condition Q-linear convergence is shown to be almost sure from all initial points that are sufficiently c,lose to x*. The possibility of significantly better performance by other nonlienar equation solvers is ruled out. Instead convergence acceleration is achieved by variation of the stepsize or Richardson extrapolation. If...[Show more]

CollectionsOpen Access Theses
Date published: 1980
Type: Thesis (PhD)


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