{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,6]],"date-time":"2025-05-06T08:25:30Z","timestamp":1746519930959},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"3-4","license":[{"start":{"date-parts":[[2006,10,7]],"date-time":"2006-10-07T00:00:00Z","timestamp":1160179200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2006,11,13]]},"DOI":"10.1007\/s11075-006-9041-7","type":"journal-article","created":{"date-parts":[[2006,10,6]],"date-time":"2006-10-06T10:27:49Z","timestamp":1160130469000},"page":"247-280","source":"Crossref","is-referenced-by-count":9,"title":["Bounds for the Perron root, singularity\/nonsingularity conditions, and eigenvalue inclusion sets"],"prefix":"10.1007","volume":"42","author":[{"given":"Lilia Yu.","family":"Kolotilina","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2006,10,7]]},"reference":[{"key":"9041_CR1","first-page":"635","volume":"58","author":"Y.A. Al\u2019pin","year":"1995","unstructured":"Al\u2019pin, Y.A.: Bounds for the Perron root of a nonnegative matrix, involving properties of its graph. Mat. Zametki 58, 635\u2013637 (1995)","journal-title":"Mat. Zametki"},{"key":"9041_CR2","volume-title":"Nonnegative Matrices in the Mathematical Sciences","author":"A. Berman","year":"1969","unstructured":"Berman, A., Plemmons, R.: Nonnegative Matrices in the Mathematical Sciences. Academic Press, New York (1969)"},{"key":"9041_CR3","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1215\/S0012-7094-47-01403-8","volume":"14","author":"A. Brauer","year":"1947","unstructured":"Brauer, A.: Limits for the characteristic roots of a matrix: II. Duke Math. J. 14, 21\u201326 (1947)","journal-title":"Duke Math. J."},{"key":"9041_CR4","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1215\/S0012-7094-52-01910-8","volume":"19","author":"A. Brauer","year":"1952","unstructured":"Brauer, A.: Limits for the characteristic roots of a matrix: IV. Duke Math. J. 19, 75\u201391 (1952)","journal-title":"Duke Math. J."},{"key":"9041_CR5","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/0024-3795(74)90048-2","volume":"8","author":"A. Brauer","year":"1974","unstructured":"Brauer, A., Gentry, I.C.: Bounds for the greatest characteristic root of an irreducible nonnegative matrix. Linear Algebra Appl. 8, 105\u2013107 (1974)","journal-title":"Linear Algebra Appl."},{"key":"9041_CR6","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1080\/03081088208817439","volume":"11","author":"R. Brualdi","year":"1982","unstructured":"Brualdi, R.: Matrices, eigenvalues, and directed graphs. Linear Multilinear Algebra 11, 143\u2013165 (1982)","journal-title":"Linear Multilinear Algebra"},{"key":"9041_CR7","first-page":"73","volume":"18","author":"L. Cvetkovi\u0107","year":"2004","unstructured":"Cvetkovi\u0107, L., Kosti\u0107, V., Varga, R.S.: A new Ger $\\breve{{\\text{s}}}$ gorin-type eigenvalue inclusion set. Electron. Trans. Numer. Anal. 18, 73\u201380 (2004)","journal-title":"Electron. Trans. Numer. Anal."},{"key":"9041_CR8","doi-asserted-by":"crossref","first-page":"428","DOI":"10.21136\/CMJ.1969.100913","volume":"19","author":"M. Fiedler","year":"1969","unstructured":"Fiedler, M., Pt\u00e1k, V.: Cyclic products and an inequality for determinants. Czechoslov. Math J. 19, 428\u2013450 (1969)","journal-title":"Czechoslov. Math J."},{"key":"9041_CR9","unstructured":"Frobenius, G.: \u00dcber Matrizen aus nicht negativen Elementen. Sitz.ber. Preuss. Akad. Wiss. Berl. 456\u2013477 (1912)"},{"key":"9041_CR10","first-page":"749","volume":"1","author":"S. Gerschgorin","year":"1931","unstructured":"Gerschgorin, S.: \u00dcber die Abgrenzung der Eigenwerte einer Matrix. Izv. Akad. Nauk SSSR, Ser. Mat. 1, 749\u2013754 (1931)","journal-title":"Izv. Akad. Nauk SSSR, Ser. Mat."},{"key":"9041_CR11","unstructured":"Gudkov, V.V.: On a certain test for nonsingularity of matrices. Latvian Math. Yearbook. 385\u2013390 (1965)"},{"key":"9041_CR12","doi-asserted-by":"crossref","DOI":"10.21236\/AD0705364","volume-title":"Graph Theory","author":"F. Harary","year":"1969","unstructured":"Harary, F.: Graph Theory. Addison-Wesley, Reading, Massachusetts (1969)"},{"key":"9041_CR13","first-page":"77","volume":"284","author":"L.Y. Kolotilina","year":"2002","unstructured":"Kolotilina, L.Y.: Bounds and inequalities for the Perron root of a nonnegative matrix. Zap. Nauchn. Semin. POMI 284, 77\u2013122 (2002)","journal-title":"Zap. Nauchn. Semin. POMI"},{"key":"9041_CR14","first-page":"48","volume":"284","author":"L.Y. Kolotilina","year":"2002","unstructured":"Kolotilina, L.Y.: On Brualdi\u2019s theorem. Zap. Nauchn. Semin. POMI 284, 48\u201363 (2002)","journal-title":"Zap. Nauchn. Semin. POMI"},{"key":"9041_CR15","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/S0024-3795(02)00422-6","volume":"359","author":"L.Y. Kolotilina","year":"2003","unstructured":"Kolotilina, L.Y.: Nonsingularity\/singularity criteria for block diagonally dominant matrices. Linear Algebra Appl. 359, 133\u2013159 (2003)","journal-title":"Linear Algebra Appl."},{"key":"9041_CR16","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/S0024-3795(02)00537-2","volume":"364","author":"L.Y. Kolotilina","year":"2003","unstructured":"Kolotilina, L.Y.: Generalizations of the Ostrowski\u2013Brauer theorem. Linear Algebra Appl. 364, 65\u201380 (2003)","journal-title":"Linear Algebra Appl."},{"key":"9041_CR17","first-page":"60","volume":"296","author":"L.Y. Kolotilina","year":"2003","unstructured":"Kolotilina, L.Y.: Bounds and inequalities for the Perron root of a nonnegative matrix. II. Circuit bounds and inequalities. Zap. Nauchn. Semin. POMI 296, 60\u201388 (2003)","journal-title":"Zap. Nauchn. Semin. POMI"},{"key":"9041_CR18","first-page":"40","volume":"309","author":"L.Y. Kolotilina","year":"2004","unstructured":"Kolotilina, L.Y.: The singularity\/nonsingularity problem for matrices satisfying diagonal dominance conditions in terms of directed graphs. Zap. Nauchn. Semin. POMI 309, 40\u201383 (2004)","journal-title":"Zap. Nauchn. Semin. POMI"},{"key":"9041_CR19","first-page":"69","volume":"323","author":"L.Y. Kolotilina","year":"2005","unstructured":"Kolotilina, L.Y.: Bounds and inequalities for the Perron root of a nonnegative matrix. III. Bounds dependent on simple paths and circuits. Zap. Nauchn. Semin. POMI 323, 69\u201393 (2005)","journal-title":"Zap. Nauchn. Semin. POMI"},{"key":"9041_CR20","first-page":"94","volume":"323","author":"L.Y. Kolotilina","year":"2005","unstructured":"Kolotilina, L.Y.: Pseudoblock conditions of diagonal dominance. Zap. Nauchn. Semin. POMI 323, 94\u2013131 (2005)","journal-title":"Zap. Nauchn. Semin. POMI"},{"key":"9041_CR21","doi-asserted-by":"crossref","unstructured":"Kolotilina, L.Y.: Filling the gap between the Gerschgorin and Brualdi theorems. Zap. Nauchn. Semin. POMI (in press)","DOI":"10.1007\/s10958-007-0074-9"},{"key":"9041_CR22","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/S0024-3795(96)90008-7","volume":"239","author":"S.-L. Liu","year":"1996","unstructured":"Liu, S.-L.: Bounds for the greatest characteristic root of a nonnegative matrix. Linear Algebra Appl. 239, 151\u2013160 (1996)","journal-title":"Linear Algebra Appl."},{"key":"9041_CR23","volume-title":"A Survey of Matrix Theory and Matrix Inequalities","author":"M. Marcus","year":"1964","unstructured":"Marcus, M., Minc, H.: A Survey of Matrix Theory and Matrix Inequalities. Prindle, Weber and Schmidt, Boston, Massachusetts (1964)"},{"key":"9041_CR24","volume-title":"Nonnegative Matrices","author":"H. Minc","year":"1988","unstructured":"Minc, H.: Nonnegative Matrices. John Wiley & Sons, New York (1988)"},{"key":"9041_CR25","first-page":"209","volume":"9","author":"A.M. Ostrowski","year":"1951","unstructured":"Ostrowski, A.M.: \u00dcber das Nichtverschwinden einer Klasse von Determinanten und die Lokalisierung der characterisrichen Wurzeln von Matrizen. Compos. Math. 9, 209\u2013226 (1951)","journal-title":"Compos. Math."},{"key":"9041_CR26","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/0022-247X(61)90030-0","volume":"2","author":"A.M. Ostrowski","year":"1961","unstructured":"Ostrowski, A.M.: On some metrical properties of operator matrices and matrices partitioned into blocks. J. Math. Anal. Appl. 2, 161\u2013209 (1961)","journal-title":"J. Math. Anal. Appl."},{"key":"9041_CR27","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1002\/zamm.19670470710","volume":"47","author":"H.J. Rein","year":"1967","unstructured":"Rein, H.J.: Bemerkung zu einem Satz von A. Brauer. Kleine Mitt. Z. Angew. Math. Mech. 47, 475\u2013476 (1967)","journal-title":"Brauer. Kleine Mitt. Z. Angew. Math. Mech."},{"key":"9041_CR28","volume-title":"Springer Series in Computational Mathematics, vol. 36","author":"R.S. Varga","year":"2004","unstructured":"Varga, R.S.: Ger\u0161gorin and His Circles. In: Springer Series in Computational Mathematics, vol. 36. Springer, Berlin Heidelberg New York (2004)"},{"key":"9041_CR29","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/0024-3795(94)90321-2","volume":"196","author":"Z. Xian","year":"1994","unstructured":"Xian, Z., Dunhe, G.: A note on A. Brauer\u2019s theorem. Linear Algebra Appl. 196, 163\u2013174 (1994)","journal-title":"Linear Algebra Appl."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-006-9041-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-006-9041-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-006-9041-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,8,1]],"date-time":"2021-08-01T22:46:10Z","timestamp":1627857970000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-006-9041-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,10,7]]},"references-count":29,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2006,11,13]]}},"alternative-id":["9041"],"URL":"https:\/\/doi.org\/10.1007\/s11075-006-9041-7","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,10,7]]}}}