| Форма представления | Статьи в зарубежных журналах и сборниках |
| Год публикации | 2024 |
| Язык | английский |
|
Габидуллина Зульфия Равилевна, автор
|
| Библиографическое описание на языке оригинала |
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. |
| Аннотация |
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. |
| Ключевые слова |
adaptive steepest descent method, matrix norm, Perron-
Frobenius root, spectral radius, dominant eigenvalue |
| Название журнала |
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 |
| Пожалуйста, используйте этот идентификатор, чтобы цитировать или ссылаться на эту карточку |
https://repository.kpfu.ru/?p_id=302719 |
Полная запись метаданных  |
| Поле DC |
Значение |
Язык |
| dc.contributor.author |
Габидуллина Зульфия Равилевна |
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/?p_id=302719 |
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 |
Статьи в зарубежных журналах и сборниках |
ru_RU |
|
EN 
中文 
ES 
Карта сайта
