| Form of presentation | Articles in international journals and collections |
| Year of publication | 2024 |
| Язык | английский |
|
Gabidullina Zulfiya Ravilevna, author
|
| Bibliographic description in the original language |
Gabidullina Z.R., Assessing the Perron-Frobenius Root of Symmetric Positive Semidefinite Matrices by the Adaptive Steepest Descent Method//Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). - 2024. - Vol.14766 LNCS, Is.. - P.39-54. |
| Annotation |
We discuss the maximum eigenvalue problem which is fundamental
in many cutting-edge research fields. We provide the necessary
theoretical background required for applying the fully adaptive steepest
descent method (or ASDM) to estimate the Perron-Frobenius root of
symmetric positive semidefinite matrices. We reduce the problem of assessing
the Perron-Frobenius root of a certain matrix to the problem of
unconstrained optimization of the quadratic function associated with this
matrix. We experimentally investigated the ability of ASDM to approximate
the Perron-Frobenius root and carry out a comparative analysis of
the obtained computational results with some others presented earlier in
the literature. This study also provides some insight into the choice of
parameters, which are computationally important, for ASDM. The study
revealed that ASDM is suitable for estimating the Perron-Frobenius root
of matrices regardless of whether or not their elements are positive and
regardless of the dimension of these matrices. |
| Keywords |
adaptive steepest descent method, matrix norm, Perron-
Frobenius root, spectral radius, dominant eigenvalue |
| The name of the journal |
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
|
| URL |
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85198438257&doi=10.1007%2f978-3-031-62792-7_3&partnerID=40&md5=a45c02cd3772745d5a1e46b43940f898 |
| Please use this ID to quote from or refer to the card |
https://repository.kpfu.ru/eng/?p_id=302719&p_lang=2 |
Full metadata record  |
| Field DC |
Value |
Language |
| dc.contributor.author |
Gabidullina Zulfiya Ravilevna |
ru_RU |
| dc.date.accessioned |
2024-01-01T00:00:00Z |
ru_RU |
| dc.date.available |
2024-01-01T00:00:00Z |
ru_RU |
| dc.date.issued |
2024 |
ru_RU |
| dc.identifier.citation |
Gabidullina Z.R., Assessing the Perron-Frobenius Root of Symmetric Positive Semidefinite Matrices by the Adaptive Steepest Descent Method//Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). - 2024. - Vol.14766 LNCS, Is.. - P.39-54. |
ru_RU |
| dc.identifier.uri |
https://repository.kpfu.ru/eng/?p_id=302719&p_lang=2 |
ru_RU |
| dc.description.abstract |
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
ru_RU |
| dc.description.abstract |
We discuss the maximum eigenvalue problem which is fundamental
in many cutting-edge research fields. We provide the necessary
theoretical background required for applying the fully adaptive steepest
descent method (or ASDM) to estimate the Perron-Frobenius root of
symmetric positive semidefinite matrices. We reduce the problem of assessing
the Perron-Frobenius root of a certain matrix to the problem of
unconstrained optimization of the quadratic function associated with this
matrix. We experimentally investigated the ability of ASDM to approximate
the Perron-Frobenius root and carry out a comparative analysis of
the obtained computational results with some others presented earlier in
the literature. This study also provides some insight into the choice of
parameters, which are computationally important, for ASDM. The study
revealed that ASDM is suitable for estimating the Perron-Frobenius root
of matrices regardless of whether or not their elements are positive and
regardless of the dimension of these matrices. |
ru_RU |
| dc.language.iso |
ru |
ru_RU |
| dc.subject |
adaptive steepest descent method |
ru_RU |
| dc.subject |
matrix norm |
ru_RU |
| dc.subject |
Perron-
Frobenius root |
ru_RU |
| dc.subject |
spectral radius |
ru_RU |
| dc.subject |
dominant eigenvalue |
ru_RU |
| dc.title |
Assessing the Perron-Frobenius Root of Symmetric Positive Semidefinite Matrices by the Adaptive Steepest Descent Method |
ru_RU |
| dc.type |
Articles in international journals and collections |
ru_RU |
|
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