Geodesic
Upper bounds for $\|A^{-1}Q\|_\infty$
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXV, Tome 514 (2022), pp. 77-87 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper suggests a general approach to deriving upper bounds for $\|A^{-1}Q\|_\infty$ from those for $\|A^{-1}\|_\infty$ for matrices $A$ belonging to different subclasses of the class of nonsingular $\mathcal{H}$-matrices. The approach is applied to SDD, $S$-SDD, OBS, OB, and Nekrasov matrices. 
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     title = {Upper bounds for $\|A^{-1}Q\|_\infty$},
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L. Yu. Kolotilina. Upper bounds for $\|A^{-1}Q\|_\infty$. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXV, Tome 514 (2022), pp. 77-87. http://geodesic.mathdoc.fr/item/ZNSL_2022_514_a4/

[1] L. Yu. Kolotilina, “Psevdoblochnye usloviya diagonalnogo preobladaniya”, Zap. nauchn. semin. POMI, 323, 2005, 94–131

[2] L. Yu. Kolotilina, “Otsenki opredelitelei i obratnykh dlya nekotorykh $H$-matrits”, Zap. nauchn. semin. POMI, 346, 2007, 81–102

[3] L. Yu. Kolotilina, “Otsenki beskonechnoi normy obratnykh k matritsam Nekrasova”, Zap. nauchn. semin. POMI, 419, 2013, 111–120

[4] L. Yu. Kolotilina, “Nekotorye otsenki obratnykh, zavisyaschie ot struktury razrezhennosti matrits”, Zap. nauchn. semin. POMI, 482, 2019, 201–219

[5] L. Yu. Kolotilina, “Ob SDD$_1$ matritsakh”, Zap. nauchn. semin. POMI, 514, 2022, 88–112

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

[7] L. Cvetković, V. Kostić, R. Varga, “A new Gers̆gorin-type eigenvalue inclusion area”, ETNA, 18 (2004), 73–80 | MR

[8] Y. M. Gao, X. H. Wang, “Criteria for generalized diagonal dominant and M-matrices”, Linear Algebra Appl., 169 (1992), 257–268 | DOI | MR

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

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

[11] J. Liu, Y. Huang, F. Zhang, “The Schur complements of generalized doubly diagonally dominant matrices”, Linear Algebra Appl., 378 (2004), 231–244 | DOI | MR

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

[13] N. Morac̆a, “Upper bounds for the infinity norm of the inverse of SDD and ${\mathcal S}{\rm-SDD}$ matrices”, J. Comput. Appl. Math., 206 (2007), 666–678 | DOI | MR

[14] A. M. Ostrowski, “Über die Determinanten mit überwiegender Hauptdiagonale”, Comment. Math. Helv., 10 (1937), 69–96 | DOI | MR

[15] 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

[16] F. Robert, “Blocs-H-matrices et convergence des méthodes itérative”, Linear Algebra Appl., 2 (1969), 223–265 | DOI | MR

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

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

[19] R. S. Varga, Gers̆gorin and His Circles, Springer, 2004 | MR

[20] 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