Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
Iterative processes in the Krylov–sonneveld subspaces. / Il’in, V. P.
в: Journal of Mathematical Sciences (United States), Том 224, № 6, 08.2017, стр. 890-899.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Iterative processes in the Krylov–sonneveld subspaces
AU - Il’in, V. P.
N1 - Publisher Copyright: © 2017 Springer Science+Business Media New York.
PY - 2017/8
Y1 - 2017/8
N2 - The paper presents a generalized block version of the Induced Dimension Reduction (IDR) methods in comparison with the Multi–Preconditioned Semi-Conjugate Direction (MPSCD) algorithms in Krylov subspaces with deflation and low-rank matrix approximation. General and individual orthogonality and variational properties of these two methodologies are analyzed. It is demonstrated, in particular, that for any sequence of Krylov subspaces with increasing dimensions there exists a sequence of the corresponding shrinking subspaces with decreasing dimensions. The main conclusion is that the IDR procedures, proposed by P. Sonneveld and other authors, are not an alternative to but a further development of the general principles of iterative processes in Krylov subspaces. Bibliography: 29 titles.
AB - The paper presents a generalized block version of the Induced Dimension Reduction (IDR) methods in comparison with the Multi–Preconditioned Semi-Conjugate Direction (MPSCD) algorithms in Krylov subspaces with deflation and low-rank matrix approximation. General and individual orthogonality and variational properties of these two methodologies are analyzed. It is demonstrated, in particular, that for any sequence of Krylov subspaces with increasing dimensions there exists a sequence of the corresponding shrinking subspaces with decreasing dimensions. The main conclusion is that the IDR procedures, proposed by P. Sonneveld and other authors, are not an alternative to but a further development of the general principles of iterative processes in Krylov subspaces. Bibliography: 29 titles.
UR - http://www.scopus.com/inward/record.url?scp=85054180095&partnerID=8YFLogxK
U2 - 10.1007/s10958-017-3459-4
DO - 10.1007/s10958-017-3459-4
M3 - Article
AN - SCOPUS:85054180095
VL - 224
SP - 890
EP - 899
JO - Journal of Mathematical Sciences (United States)
JF - Journal of Mathematical Sciences (United States)
SN - 1072-3374
IS - 6
ER -
ID: 10182036