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.
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A. Neubauer, Otmar Scherzer, A Convergence Rate Result for a Steepest Descent Method and a Minimal Error Method for the Solution of Nonlinear Ill-Posed Problems. Z. Anal. Anwend. 14 (1995), no. 2, pp. 369–377DOI 10.4171/ZAA/679