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

DOI:
https://doi.org/10.1090/S0002-9939-1983-0699408-9

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:
https://doi.org/10.1090/S0002-9939-1983-0699408-9

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