123681098
Zur Theorie der elektronenoptischen Linsenfehler
ZusammenfassungIst der Verlauf des Potentials auf der optischen Achse einer elektrischen Elektronenlinse gegeben, so lassen sich die Linsenfehler und die Form der Elektroden berechnen.
120639964
Zum relativistischen Zweikörperproblem
ZusammenfassungEs wird eine Wellengleichung aufgesucht, die in erster Näherung das von Møller angegebene Matrixelement der retardierten Wechselwirkung liefert.
120227077
Convergence rates of iterated Tikhonov regularized solutions of nonlinear III — posed problems
SummaryIn this paper we investigate iterated Tikhonov regularization for the solution of nonlinear ill-posed problems. In the case of linear ill-posed problems it is well-known that (under appropriate assumptions) then-th iterated regularized solutions can converge likeO(δ22/(2n+1)), where δ denotes the noise level of the data perturbation. We give conditions that guarantee this convergence rate also for nonlinear ill-posed problems, and motivate these conditions by the mapping degree. The results are derived by a comparison of the iterated regularized solutions of the nonlinear problem with the iterated regularized solutions of its linearization. Numerical examples are presented.
121129232
A Convergence Rate Result for a Steepest Descent Method and a Minimal Error Method for the Solution of Nonlinear Ill-Posed Problems
Recently, convergence and stability of the steepest descent method for the solution of nonlinear ill-posed operator equations have been proven. The same results also hold for the minimal error method. Since for ill-posed problems the convergence of iterative methods may be arbitrarily slow, it is of practical interest to guarantee convergence rates of the iterates under reasonable assumptions. The main emphasis of this paper is to present a convergence rate result in a uniform manner for the steepest descent and the minimal error method for the noise free case.