Feedback in Iterative Algorithms

نویسنده

  • Charles Byrne
چکیده

When the nonnegative system of linear equations y = Px has no nonnegative exact solutions, block-iterative methods fail to converge, exhibiting, instead, subsequential convergence leading to a limit cycle of two or more distinct vectors. From the vectors of the limit cycle we extract new data, replace the data vector y with this new data vector, and restart the iterative process. Success with this approach as applied to the algebraic reconstruction technique (ART) prompts us to apply feedback to other block-iterative methods. We consider here several questions pertaining to this feedback approach: Can we show the existence of limit cycles for these other block-iterative algorithms? Does the sequence of successive limit cycles converge to a single vector? If so, which vector is it?

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تاریخ انتشار 2005