A Convergence Rate Result for a Steepest Descent Method and a Minimal Error Method for the Solution of Nonlinear Ill-Posed Problems | Zendy

Andreas B. Neubauer | Zendy; Otmar Scherzer | Zendy

Open Access

A Convergence Rate Result for a Steepest Descent Method and a Minimal Error Method for the Solution of Nonlinear Ill-Posed Problems

Author(s) -

Andreas B. Neubauer,

Otmar Scherzer

Publication year - 1995

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/679

Subject(s) - method of steepest descent , descent (aeronautics) , rate of convergence , mathematics , nonlinear system , convergence (economics) , well posed problem , gradient descent , mathematical optimization , computer science , artificial neural network , physics , economics , artificial intelligence , key (lock) , quantum mechanics , economic growth , computer security , meteorology

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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