Existence and approximation of solutions for Fredholm equations of the first kind with applications to a linear moment problem

Authors:
Dan Butnariu;Ben Zion Shklyar
Affiliations:
Department of Mathematics, University of Haifa, Haifa, Israel;Holon Institute of Technology, Holon, Israel
Venue:
Optimization Methods & Software
Year:
2008

Citing 5
Cited 1

Mobile control of distributed parameter systems

Mobile control of distributed parameter systems
Successive averages of firmly nonexpansive mappings

Mathematics of Operations Research
On Projection Algorithms for Solving Convex Feasibility Problems

SIAM Review
Iterative Methods of Solving Stochastic Convex Feasibility Problems andApplications

Computational Optimization and Applications
Differential Inclusions: Set-Valued Maps and Viability Theory

Differential Inclusions: Set-Valued Maps and Viability Theory

Enlarged cores and bargaining schemes in games with fuzzy coalitions

Fuzzy Sets and Systems

Quantified Score

Hi-index	0.00

Visualization

Abstract

The Cimmino algorithm is an interative projection method for finding almost common points of measurable families of closed convex sets in a Hilbert space. When applied to Fredholm equations of the first kind, the Cimmino algorithm produces weak approximations of solutions provided that solutions exist. We show that for consistent Fredholm equations of the first kind whose data satisfy some spectral conditions, the sequences produced by the Cimmino algorithm converge not only weakly but also in norm. Using this fact, we obtain an existence criterion for solutions to a class of moment problems and show that if problems in this class have solutions, then the Cimmino algorithm generate norm approximations of such solutions.