Appl Math Optim 38:45–68 (1998)
1998 Springer-Verlag New York Inc.
A Modiﬁed Landweber Iteration for Solving
Parameter Estimation Problems
Institut f¨ur Mathematik, Universit¨at Linz,
Altenberger Strasse 69, A-4040 Linz, Austria
Abstract. In this paper a convergence analysis for a modiﬁed Landweber iteration
for the solution of nonlinear ill-posed problems is presented. A priori and a posteriori
stopping criteria for terminating the iteration are compared. Some numerical results
for the solution of a parameter estimation problem are presented.
Key Words. Nonlinear ill-posed problems, Modiﬁed Landweber iteration, Regu-
larization methods, Stopping rules.
AMS Classiﬁcation. 65J15, 65J20, 47H17.
This paper is concerned with nonlinear operator equations
F(x) = y, (1.1)
where F: D(F) → Y with domain D(F) ⊆ X. We restrict our attention to real Hilbert
space X and Y with inner products (·,·) and norms ·, respectively; they can always
be identiﬁed from the context in which they appear.
Throughout the paper it is assumed that the data y in (1.1) is attainable, i.e., that
(1.1) has a solution x
(which need not be unique).
This research was supported in part by the Christian-Doppler Society, Austria. The author’s stay at
the Department of Mathematical Sciences, University of Delaware, is supported by the Austrian Fonds zur
F¨orderung der Wissenschaftlichen Forschung, Grant J01088-TEC.
Present Address: Department of Mathematical Sciences, University of Delaware, Newark, DE 19716,