Investigation of the stability of simple quasi-Toeplitz tridiagonal systems with unlimited dimension
The Bulletin of Irkutsk State University. Series Mathematics, Tome 6 (2013) no. 3, pp. 25-37 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Investigation of quasi-Toeplitz tridiagonal systems of linear algebraic equations in the case where the dimension of unlimited increases. Proved theorem on the stability of the systems, which does not coincide with previously known conditions. Is an example that shows that the obtained sufficient conditions for stability are close to being necessary.
Keywords: systems of linear algebraic equations; tridiagonal matrix; quasi-Toeplitz matrix; stability.
@article{IIGUM_2013_6_3_a1,
     author = {A. L. Kazakov and T. A. Batagaeva},
     title = {Investigation of the stability of simple {quasi-Toeplitz} tridiagonal systems with unlimited dimension},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {25--37},
     year = {2013},
     volume = {6},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2013_6_3_a1/}
}
TY  - JOUR
AU  - A. L. Kazakov
AU  - T. A. Batagaeva
TI  - Investigation of the stability of simple quasi-Toeplitz tridiagonal systems with unlimited dimension
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2013
SP  - 25
EP  - 37
VL  - 6
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2013_6_3_a1/
LA  - ru
ID  - IIGUM_2013_6_3_a1
ER  - 
%0 Journal Article
%A A. L. Kazakov
%A T. A. Batagaeva
%T Investigation of the stability of simple quasi-Toeplitz tridiagonal systems with unlimited dimension
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2013
%P 25-37
%V 6
%N 3
%U http://geodesic.mathdoc.fr/item/IIGUM_2013_6_3_a1/
%G ru
%F IIGUM_2013_6_3_a1
A. L. Kazakov; T. A. Batagaeva. Investigation of the stability of simple quasi-Toeplitz tridiagonal systems with unlimited dimension. The Bulletin of Irkutsk State University. Series Mathematics, Tome 6 (2013) no. 3, pp. 25-37. http://geodesic.mathdoc.fr/item/IIGUM_2013_6_3_a1/

[1] N. S. Bakhvalov, N. P. Zhidkov, G. M. Kobelnikov, Chislennye metody, Binomyu Laboratoriya znanii, M., 2003, 632 pp.

[2] B. Bukhberger, G. A. Emelyanenko, “Metody obrascheniya trekhdiagonalnykh matrits”, Zhurn. vychisl. matematiki i mat. fiziki, 13:3 (1973), 546–554

[3] F. R. Gantmakher, Teoriya matrits, 5-e izd.,, Fizmatlit, M., 2004, 560 pp.

[4] S. K. Godunov, A. N. Malyshev, “O spetsialnom bazise iz priblizhennykh sobstvennykh vektorov s lokalizovannymi nositelyami dlya izolirovannogo uzkogo klastera sobstvennykh znachenii simmetrichnoi trekhdiagonalnoi matritsy”, Zhurn. vychisl. matematiki i mat. fiziki, 48:7 (2008), 1156–1166 | MR

[5] S. K. Godunov, V. S. Ryabenkii, Raznostnye skhemy (vvedenie v teoriyu), Nauka, M., 1977, 440 pp. | MR

[6] V. P. Ilin, Yu. I. Kuznetsov, Trekhdiagonalnye matritsy i ikh prilozheniya, Nauka, M., 1985, 208 pp. | MR

[7] A. L. Kazakov, A. A. Lempert, “Analiticheskoe i chislennoe issledovanie obobschennykh zadach Koshi, voznikayuschikh v gazovoi dinamike”, Prikl. mekhanika i tekhn. fizika, 52:3 (2011), 30–40 | MR

[8] S. K. Lando, Lektsii o proizvodyaschikh funktsiyakh, MTsNMO, M., 2002, 144 pp.

[9] A. F. Sidorov, Izbrannye trudy. Matematika. Mekhanika, Fizmatlit, M., 2001, 576 pp. | MR

[10] R. Alvarez-Nodarse, J. Petronilho, N. R. Quintero, “Spectral properties of certain tridiagonal matrices”, Linear Algebra and its Applications, 436 (2012), 682–698 | DOI | MR

[11] J. R. Bunch, R. F. Marcia, “A pivoting strategy for symmetric tridiagonal matrices”, Numerical Linear Algebra with Applications, 13 (2006), 865–867 | DOI | MR

[12] M. A. El-Shehawey, Gh. A. El-Shreef, A. Sh. Al-Henawy, “Analytical inversion of general periodic tridiagonal matrices”, Journal of Mathematical Analysis and Applications, 345 (2008), 123–134 | DOI | MR

[13] C. M. Da Fonseca, J. Petronilho, “Explicit inverse of a tridiagonal $k$-Toeplitz matrix”, Numerische Mathematik, 100 (2005), 457–482 | DOI | MR

[14] C. M. Da Fonseca, J. Petronilho, “Explicit inverses of some tridiagonal matrices”, Linear Algebra and its Applications, 325 (2001), 7–21 | DOI | MR

[15] Y. Huang, W. F. McColl, “Analytical inversion of general tridiagonal matrices”, Journal of Physics A: Mathematical and Theoretical, 1997, 7919–7933 | DOI | MR

[16] G. A. Meurant, “Review on inverse of symmetric tridiagonal and block tridiagonal matrices”, The SIAM Journal on Matrix Analysis and Applications, 13:1 (1992), 707–728 | DOI | MR

[17] R. Vandebril, M. V. Barel, N. Mastronardi, Matrix Computations and Semiseparable Matrices, v. 2, 2008, 498 pp.

[18] W. Ch. Yueh, “Explicit Inverses Of Several Tridiagonal Matrices”, Applied Mathematics E-Notes, 6 (2006), 74–83 | MR