On the Forsythe conjecture
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10472976" target="_blank" >RIV/00216208:11320/23:10472976 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=yhUsUGzRWV" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=yhUsUGzRWV</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10543-023-00991-x" target="_blank" >10.1007/s10543-023-00991-x</a>
Alternative languages
Result language
angličtina
Original language name
On the Forsythe conjecture
Original language description
Forsythe formulated a conjecture about the asymptotic behavior of the restarted conjugate gradient method in 1968. We translate several of his results into modern terms, and pose an analogous version of the conjecture (originally formulated only for symmetric positive definite matrices) for symmetric and nonsymmetric matrices. Our version of the conjecture uses a two-sided or cross iteration with the given matrix and its transpose, which is based on the projection process used in the Arnoldi (or for symmetric matrices the Lanczos) algorithm. We prove several new results about the limiting behavior of this iteration, but the conjecture still remains largely open. We hope that our paper motivates further research that eventually leads to a proof of the conjecture.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA20-01074S" target="_blank" >GA20-01074S: Adaptive methods for the numerical solution of partial differential equations: analysis, error estimates and iterative solvers</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
BIT Numerical Mathematics
ISSN
0006-3835
e-ISSN
1572-9125
Volume of the periodical
63
Issue of the periodical within the volume
4
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
27
Pages from-to
49
UT code for WoS article
001077631200001
EID of the result in the Scopus database
2-s2.0-85173114655