We first provide a simple estimate for || A-1||∞and||A-1||1 of a strictly diagonally dominant matrix A. On the Basis of the result, we obtain an estimate for the smallest singular value of A. Secondly, by scaling with a positive diagonal matrix D, we obtain some simple estimates for the smallest singular value of an H-matrix, which is not necessarily positive definite. Finally, we give some examples to show the effectiveness of the new bounds.
Chuan-long WANG, Guo-jian ZHANGDepartment of Mathematics, Normal College of Shanxi University, Taiyuan 030012, ChinaDepartment of Applied Mathematics, Taiyuan University of Technology, Taiyuan, 030024, China
