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Iterative processes in the Krylov–sonneveld subspaces. / Il’in, V. P.

In: Journal of Mathematical Sciences (United States), Vol. 224, No. 6, 08.2017, p. 890-899.

Research output: Contribution to journal › Article › peer-review

Harvard

Il’in, VP 2017, 'Iterative processes in the Krylov–sonneveld subspaces', Journal of Mathematical Sciences (United States), vol. 224, no. 6, pp. 890-899. https://doi.org/10.1007/s10958-017-3459-4

APA

Il’in, V. P. (2017). Iterative processes in the Krylov–sonneveld subspaces. Journal of Mathematical Sciences (United States), 224(6), 890-899. https://doi.org/10.1007/s10958-017-3459-4

Vancouver

Il’in VP. Iterative processes in the Krylov–sonneveld subspaces. Journal of Mathematical Sciences (United States). 2017 Aug;224(6):890-899. doi: 10.1007/s10958-017-3459-4

Author

Il’in, V. P. / Iterative processes in the Krylov–sonneveld subspaces. In: Journal of Mathematical Sciences (United States). 2017 ; Vol. 224, No. 6. pp. 890-899.

BibTeX

@article{b511a7fe4ccf447a97c39bb6a5b3f958,
title = "Iterative processes in the Krylov–sonneveld subspaces",
abstract = "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.",
author = "Il{\textquoteright}in, {V. P.}",
note = "Publisher Copyright: {\textcopyright} 2017 Springer Science+Business Media New York.",
year = "2017",
month = aug,
doi = "10.1007/s10958-017-3459-4",
language = "English",
volume = "224",
pages = "890--899",
journal = "Journal of Mathematical Sciences (United States)",
issn = "1072-3374",
publisher = "Springer Nature",
number = "6",

}

RIS

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