On Diagonal Dominance Arguments for Bounding the Norm of the Inverse Matrix (A) sub Infinity,
KENT STATE UNIV OHIO DEPT OF MATHEMATICS
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In a recent paper by J. M. Varah, an upper bound for the norm of the inverse matrix A sub infinity was determined, under the assumption that A is strictly diagonally dominant, and this bound was then used to obtain a lower bound for the smallest singular value for A. In this note, this upper bound for the norm of the inverse matrix A sub infinity is sharpened, and extended to a wider class of matrices. This bound is then used to obtain an improved lower bound for the smallest singular value of a matrix.
- Theoretical Mathematics