Renormalised steepest descent in Hilbert space converges to a two-point attractor
UNSPECIFIED. (2001) Renormalised steepest descent in Hilbert space converges to a two-point attractor. ACTA APPLICANDAE MATHEMATICAE, 67 (1). pp. 1-18. ISSN 0167-8019Full text not available from this repository.
The result that for quadratic functions the classical steepest descent algorithm in R-d converges locally to a two-point attractor was proved by Akaike. In this paper this result is proved for bounded quadratic operators in Hilbert space. The asymptotic rate of convergence is shown to depend on the starting point while, as expected, confirming the Kantorovich bounds. The introduction of a relaxation coefficient in the steepest-descent algorithm completely changes its behaviour, which may become chaotic. Different attractors are presented. We show that relaxation allows a significantly improved rate of convergence.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Journal or Publication Title:||ACTA APPLICANDAE MATHEMATICAE|
|Publisher:||KLUWER ACADEMIC PUBL|
|Official Date:||May 2001|
|Number of Pages:||18|
|Page Range:||pp. 1-18|
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