Geodesic
Upper bounds for $\|A^{-1}\|_\infty$ for some eventually $\mathcal{H}$-matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXVI, Tome 524 (2023), pp. 64-73 
L. Yu. Kolotilina. Upper bounds for $\|A^{-1}\|_\infty$ for some eventually $\mathcal{H}$-matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXVI, Tome 524 (2023), pp. 64-73. http://geodesic.mathdoc.fr/item/ZNSL_2023_524_a5/
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     author = {L. Yu. Kolotilina},
     title = {Upper bounds for $\|A^{-1}\|_\infty$ for some eventually $\mathcal{H}$-matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {64--73},
     year = {2023},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2023_524_a5/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The paper suggests two general approaches to deriving upper bounds for $\|A^{-1}\|_\infty$ for some eventually $\mathcal{H}$-matrices $A$. The approaches are illustrated by considering the classes of eventually SDD and eventually DSDD matrices, for which improvements of the known bounds are derived. Also it is indicated that the approaches suggested are actually applicable to considerably larger matrix classes.

[1] L. Yu. Kolotilina, “Nekotorye novye klassy nevyrozhdennykh matrits i verkhnie otsenki dlya ikh obratnykh”, Zap. nauchn. semin. POMI, 482, 2019, 184–200

[2] L. Yu. Kolotilina, “Verkhnie otsnki dlya $\|A^{-1}Q\|_\infty$”, Zap. nauchn. semin. POMI, 514, 2022, 77–87

[3] J. H. Ahlberg, E. N. Nilson, “Convergence properties of the spline fit”, J. Soc. Ind. Appl. Math., 11 (1963), 95–104 | DOI | MR | Zbl

[4] L. Cvetković, M. Erić, J. M. Peña, “Eventually SDD matrices and eigenvalue localization”, Appl. Math. Comput., 252 (2015), 535–540 | MR | Zbl

[5] V. R. Kostić, L. Cvetković, D. I. Cvetković, “Pseudospectra localization and their applications”, Numer. Linear Algebra Appl., 23 (2016), 356–372 | DOI | MR | Zbl

[6] Y. Li, Y. Wang, “Schur complement-based infinity norm bounds for the inverse of GDSDD matrices”, Mathematics, 10 (2022), 186 | DOI | MR | Zbl

[7] J. Liu, J. Zhang, Y. Liu, “The Schur complement of strictly doubly diagonally dominant matrices and its application”, Linear Algebra Appl., 437 (2012), 168–183 | DOI | MR | Zbl

[8] A. Melman, “Ovals of Cassini for Toeplitz matrices”, Linear Multilinear Algebra, 60 (2012), 189–199 | DOI | MR | Zbl

[9] S. Z. Pan, S. C. Chen, “An upper bound for $\|A^{-1} \|_\infty$ of strictly doubly diagonally dominant matrices”, J. Fuzhou Univ. Nat. Sci. Ed., 36 (2008), 639–642 (in Chinese) | MR

[10] C. Sang, “Schur complement-based infinity norm bounds for the inverse of $DSDD$ matrices”, Bull. Iran. Math. Soc., 47 (2020), 1379–1398 | DOI | MR

[11] C. Sang, J. X. Zhao, “Eventually DSDD matrices and eigenvalue localization”, Symmetry, 448:10 (2018) | DOI

[12] J. M. Varah, “A lower bound for the smallest singular value of a matrix”, Linear Algebra Appl., 11 (1975), 3–5 | DOI | MR | Zbl

[13] X. R. Yong, “Two properties of diagonally dominant matrices”, Numer. Linear Algebra, 3 (1996), 173–177 | 3.0.CO;2-C class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl