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Perturbation of invariant subspaces
Mathematical Communications, 1 (1996), 1; 51-59. urn:nbn:hr:133:950574
Truhar, Ninoslav

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Truhar, N. (1996). Perturbation of invariant subspaces. Mathematical Communications, 1. (1), 51-59. Retrieved from https://urn.nsk.hr/urn:nbn:hr:133:950574

Truhar, Ninoslav. "Perturbation of invariant subspaces." Mathematical Communications, vol. 1, no. 1, 1996, pp. 51-59. https://urn.nsk.hr/urn:nbn:hr:133:950574

Truhar, Ninoslav. "Perturbation of invariant subspaces." Mathematical Communications 1, no. 1 (1996): 51-59. https://urn.nsk.hr/urn:nbn:hr:133:950574

Truhar, N. (1996) 'Perturbation of invariant subspaces', Mathematical Communications, 1(1), pp. 51-59. Available at: https://urn.nsk.hr/urn:nbn:hr:133:950574 (Accessed 24 December 2024)

Truhar N. Perturbation of invariant subspaces. Mathematical Communications [Internet]. 1996 [cited 2024 December 24];1(1):51-59. Available at: https://urn.nsk.hr/urn:nbn:hr:133:950574

N. Truhar, "Perturbation of invariant subspaces", Mathematical Communications, vol. 1, no. 1, pp. 51-59, 1996. [Online]. Available at: https://urn.nsk.hr/urn:nbn:hr:133:950574. [Accessed: 24 December 2024]

Metadata
Title (english)Perturbation of invariant subspaces
Title (croatian)Perturbacija invarijantnih potprostora
AuthorNinoslav Truhar
Author's institutionJosip Juraj Strossmayer University of Osijek
Faculty of Civil Engineering and Architecture Osijek
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract (english)
We consider two different theoretical approaches for the problem of the perturbation of invariant subspaces. The first approach belongs to the standard theory. In that approach the bounds for the norm of the perturbation of the projector are proportional to the norm of perturbation matrix, and inversely proportional to the distance between the corresponding eigenvalues and the rest of the spectrum. The second approach belongs to the relative theory which deals only with Hermitian matrices. The bounds which result from this approach are proportional to the size of relative perturbation of matrix elements and the condition number of a scaled matrix, and inversely proportional to the relative gap between the corresponding eigenvalue and the rest of the spectrum. Because of a relative gap these bounds are in some cases less pessimistic than the standard norm estimates.
Abstract (croatian)
Prikazana su dva teorijska pristupa koji se bave problemom perturbacija invarijantnih potprostora. Veličina perturbacije mjeri se normom pripadnih projektora, jer projektori ne ovise o izboru baza promatranih potprostora. Prvi pristup pripada standardnoj perturbacijskoj teoriji. U tom pristupu ocjene za normu perturbacije projektora proporcionalne su normi matrice perturbacije, a obrnuto proporcionalne udaljenosti odgovarajuće svojstvene vrijednosti od ostatka spektra. Drugi pristup pripada tzv. relativnoj perturbacijskoj teoriji, koja promatra samo perturbacije invarijantnih potprostora hermitskih matrica. Ocjene koje slijede iz tog pristupa proporcionalne su veličini relativne promjene matričnih elemenata i uvjetovanosti skalirane matrice, a obrnuto proporcionalne s relativnom udaljenošću odgovarajuće svojstvene vrijednosti od ostatka spektra. Zbog relativne udaljenosti u nekim situacijama relativne perturbacijske ocjene manje su pesimistične od ocjena standardne perturbacijske teorije.
Keywords (english)
Keywords (croatian)
Languageenglish
Publication typeProfessional paper - Professional paper
Publication statusPublished
Peer reviewPeer review
Publication versionPublished version
Journal titleMathematical Communications
Numberingvol. 1, no. 1, pp. 51-59
p-ISSN1331-0623
e-ISSN1848-8013
URN:NBNurn:nbn:hr:133:950574
Publication1996
Document URLhttps://hrcak.srce.hr/1851
Type of resourceText
Access conditionsOpen access
Terms of useLicence Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) icon
Created on2018-05-15 09:09:51