Geodesic
New bounds for the minimum eigenvalue of the Fan product of two $M$-matrices
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 63-68 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper, we mainly use the properties of the minimum eigenvalue of the Fan product of $M$-matrices and Cauchy-Schwarz inequality, and propose some new bounds for the minimum eigenvalue of the Fan product of two $M$-matrices. These results involve the maximum absolute value of off-diagonal entries of each row. Hence, the lower bounds for the minimum eigenvalue are easily calculated in the practical examples. In theory, a comparison is given in this paper. Finally, to illustrate our results, a simple example is also considered.
In this paper, we mainly use the properties of the minimum eigenvalue of the Fan product of $M$-matrices and Cauchy-Schwarz inequality, and propose some new bounds for the minimum eigenvalue of the Fan product of two $M$-matrices. These results involve the maximum absolute value of off-diagonal entries of each row. Hence, the lower bounds for the minimum eigenvalue are easily calculated in the practical examples. In theory, a comparison is given in this paper. Finally, to illustrate our results, a simple example is also considered.
DOI : 10.1007/s10587-014-0083-z
Classification : 15A18, 15A42, 15B48
Keywords: Fan product; minimum eigenvalue; $M$-matrix 
@article{10_1007_s10587_014_0083_z,
     author = {Cheng, Guanghui},
     title = {New bounds for the minimum eigenvalue of the {Fan} product of two $M$-matrices},
     journal = {Czechoslovak Mathematical Journal},
     pages = {63--68},
     year = {2014},
     volume = {64},
     number = {1},
     doi = {10.1007/s10587-014-0083-z},
     mrnumber = {3247444},
     zbl = {06391476},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0083-z/}
}
TY  - JOUR
AU  - Cheng, Guanghui
TI  - New bounds for the minimum eigenvalue of the Fan product of two $M$-matrices
JO  - Czechoslovak Mathematical Journal
PY  - 2014
SP  - 63
EP  - 68
VL  - 64
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0083-z/
DO  - 10.1007/s10587-014-0083-z
LA  - en
ID  - 10_1007_s10587_014_0083_z
ER  - 
%0 Journal Article
%A Cheng, Guanghui
%T New bounds for the minimum eigenvalue of the Fan product of two $M$-matrices
%J Czechoslovak Mathematical Journal
%D 2014
%P 63-68
%V 64
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0083-z/
%R 10.1007/s10587-014-0083-z
%G en
%F 10_1007_s10587_014_0083_z
Cheng, Guanghui. New bounds for the minimum eigenvalue of the Fan product of two $M$-matrices. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 63-68. doi: 10.1007/s10587-014-0083-z

Cité par Sources :