caa a22 4500 467939489 CHVBK 20180406153008.0 cr unu---uuuuu 170328e20060701xx s 000 0 eng 10.1007/s10444-004-7624-1 doi (NATIONALLICENCE)springer-10.1007/s10444-004-7624-1 Hoffman Alan Department of Mathematical Sciences, IBM Research Division, T.J. Watson Research Center, P.O. Box 218, 10598, Yorktown Heights, NY, USA aut Gersgorin variations II: On themes of Fan and Gudkov [Elektronische Daten] [Alan Hoffman] Assume F={f1,. . .,fn} is a family of nonnegative functions of n−1 nonnegative variables such that, for every matrix A of order n, |aii|>fi (moduli of off-diagonal entries in row i of A) for all i implies A nonsingular. We show that there is a positive vector x, depending only on F, such that for all A=(aij), and all i, fi≥∑j|aij|{xj}/xi. This improves a theorem of Ky Fan, and yields a generalization of a nonsingularity criterion of Gudkov. Springer, 2006 Advances in Computational Mathematics Kluwer Academic Publishers 25/1-3(2006-07-01), 1-6 1019-7168 25:1-3<1 2006 25 10444 https://doi.org/10.1007/s10444-004-7624-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10444-004-7624-1 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Hoffman Alan Department of Mathematical Sciences, IBM Research Division, T.J. Watson Research Center, P.O. Box 218, 10598, Yorktown Heights, NY, USA aut NATIONALLICENCE 773 0- Advances in Computational Mathematics Kluwer Academic Publishers 25/1-3(2006-07-01), 1-6 1019-7168 25:1-3<1 2006 25 10444 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer