Minimierung des Rechenaufwandes bei Globalisierungen spezieller Iterationsverfahren vom Typ Minimales Residuum

Local iteration methods for the solution of nonlinear operator equationsT(x)=0 can be “globalized” by the method of embedding. This means that the initial valuex ₀ need not be in the neighbourhood of a solution \(\bar x\) . We restrict ourselves to a stepwise calculation — see 17] — where one solves the chain of problems:T(x, s _i )=0, 0=s ₀<s ₁<...<s _N =1 by a local iteration method with the solutionx _i?1 ofT(x, s _i?1)=0 used as initial vector forT(x, s _i )=0. In this paper we examine methods of minimal-residue-type. Results on the minimization of the whole effort by selection of an “optimal” step width can be obtained. Furthermore, a global convergence acceleration can be reached by suitable adaption of (linear) interpolation on the step width. The reslts obtained can be transferred without difficulties to any other local iteration method which is based on the principle contraction.