On the almost strong stability of the circular deconvolution algorithm

Authors
Yalamov, PY
Citation
Py. Yalamov, On the almost strong stability of the circular deconvolution algorithm, SIAM J MATR, 22(2), 2000, pp. 358-363
Citations number
12
Categorie Soggetti
Mathematics
Journal title
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
ISSN journal
08954798 → ACNP
Volume
22
Issue
2
Year of publication
2000
Pages
358 - 363
Database
ISI
SICI code
0895-4798(20000920)22:2<358:OTASSO>2.0.ZU;2-Z
Abstract
The stability of the circular deconvolution algorithm for the solution of a circulant linear system is studied. This algorithm is known to be not stro ngly stable. The notion of almost strong stability is introduced, and it is shown that it leads to results similar to those for strongly stable algori thms. Then it is proved that the circular deconvolution algorithm based on fast Fourier transforms is almost strongly stable with respect to the 2-nor m. A numerical example illustrates the theoretical conclusions.