On the linear convergence of quasi-newton methods in finite-and infinite-dimensional Hilbert spaces

✍ Scribed by A. Lannes

• Publisher: Elsevier Science
• Year: 1980
• Tongue: English
• Weight: 415 KB
• Volume: 20
• Category: Article
• ISSN: 0010-4655
• DOI: 10.1016/0010-4655(80)90114-9

✦ Synopsis

This paper summarizes the main results concerning the analysis of the local convergence of quasi-newton methods in finite and infinite-dimensional Hilbert spaces. Although the physicist working on the computer is essentially concerned with the finite-dimensional case (i.e. the discrete case), it is often useful for him to know under which conditions the familar results can be extended verbatim to the inifinite-dimensional case (i.e. the continuous case). The analysisgiven in this paper stresses these aspects of the problem. As an example of an application, a survey of the particular quasi-Newton method that collapses to the well-known extrapolated Jacobi method in the linear case is presented. The interesting special case of holography for which the optimal parameter of relaxation is known a priori is mentioned.