Eigenvalue inclusion sets for linear response eigenvalue problems

• Autorzy: He Jun , Liu Yanmin , Lv Wei

Identyfikatory

DOI

10.1515/dema-2022-0029

• Języki publikacji: EN

Abstrakty

EN

In this article, some inclusion sets for eigenvalues of a matrix in the linear response eigenvalue problem (LREP) are established. It is proved that the inclusion sets are tighter than the Geršgorin-type sets. A numerical experiment shows the effectiveness of our new results.

Słowa kluczowe

EN

linear response eigenvalue problem; Geršgorin-type sets; localization set

PL

problem lokalizacji wartości własnych; zbiór Gerszgorina; zbiór lokalizacji; macierze

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2022
• Tom: Vol. 55, nr 1
• Strony: 380--386
• Opis fizyczny: Bibliogr. 11 poz., rys.

Twórcy

autor

He Jun

• School of Mathematics, Zunyi Normal College, Zunyi, Guizhou 563006, P. R. China

autor

Liu Yanmin

• School of Mathematics, Zunyi Normal College, Zunyi, Guizhou 563006, P. R. China

autor

Lv Wei

• School of Mathematics, Zunyi Normal College, Zunyi, Guizhou 563006, P. R. China

Bibliografia

• [1] Z. Bai and R. Li, Minimization principles for the linear response eigenvalue problem, I: Theory, SIAM J. Matrix Anal. Appl. 33 (2012), no. 4, 1075–1100, DOI: https://doi.org/10.1137/110838960.
• [2] Z. Bai and R. Li, Minimization principle for linear response eigenvalue problem, II: Computation, SIAM J. Matrix Anal. Appl. 34 (2013), no. 2, 392–416, DOI: https://doi.org/10.1137/110838972.
• [3] Z. Guo, K. Chu, and W. Lin, Doubling algorithm for the discretized Bethe-Salpeter eigenvalue problem, Math. Comp. 88 (2019), 2325–2350, DOI: https://doi.org/10.1090/mcom/3398.
• [4] Z. Bai and R. Li, Minimization principles and computation for the generalized linear response eigenvalue problem, BIT Numer. Math. 54 (2014), 31–54, DOI: https://doi.org/10.1007/s10543-014-0472-6.
• [5] D. J. Thouless, Vibrational states of nuclei in the random phase approximation, Nucl. Phys. 22 (1961), 78–95, DOI: https://doi.org/10.1016/0029-5582(61)90364-9.
• [6] A. Muta, J. Iwata, Y. Hashimoto, and K. Yabana, Solving the RPA eigenvalue equation in real-space, Progress Theor. Phys. 108 (2002), no. 6, 1065–1076, DOI: https://doi.org/10.1143/PTP.108.1065.
• [7] Z. Bai, R. Li, and W. Lin, Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods, Sci. China Math. 59 (2016), 1443–1460, DOI: https://doi.org/10.1007/s11425-016-0297-1.
• [8] H. Xu and H. Zhong, Weighted Golub-Kahan-Lanczos algorithms and applications, Electron. Trans. Numer. Anal. 47 (2017), 153–178.
• [9] R. Horn and C. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1988.
• [10] Y. Lei, W. Xu, Y. Lu, Y, Niu, and X. Gu, On the symmetric doubly stochastic inverse eigenvalue problem, Linear Algebra Appl. 445 (2014), 181–205.
• [11] G. Stewart and J. Sun, Matrix Perturbation Theory, Academic Press, New York, CA, 1990.

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).