February 2014
Intermediate to advanced
300 pages
11h 15m
English
Content preview from Iterative Optimization in Inverse Problems
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Averaged and Paracontractive Operators 101
Ex. 7.5 We say that an operator R : C
J
→ C
J
is quasi-averaged if, for
some operator Q that is qne, with respect to the two-norm, and for some α
in the interval (0, 1), we have
R =(1− α)I + αQ.
Show that the Krasnosel’skii-Mann-Opial Theorem 7.1 holds when averaged
operators are replaced by quasi-averaged operators.
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