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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Gradient method for nondensely defined closed unbounded linear operators


Authors: Sung J. Lee and M. Zuhair Nashed
Journal: Proc. Amer. Math. Soc. 88 (1983), 429-435
MSC: Primary 47A50; Secondary 65J10
MathSciNet review: 699408
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Abstract: The paper establishes the convergence of the steepest descent method for least-squares solutions of operator equations in Hilbert spaces for any (nondensely defined, unbounded) closed linear operator with closed range. This is done by using a graph topology, an explicit graph topology adjoint, and existing theory of steepest descent for bounded linear operators.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0699408-9
PII: S 0002-9939(1983)0699408-9
Keywords: Graph topology, graph topology adjoint, operator part, gradient method, steepest descent, unbounded linear operator, normal equations, iterative methods, generalized inverse of subspace
Article copyright: © Copyright 1983 American Mathematical Society