New estimates of the infinity norm bounds for the inverse of Nekrasov matrices. (Chinese. English summary) Zbl 1389.15011
Summary: The class of Nekrasov matrices is one of the important subclasses of \(H\)-matrices, it plays a key role in the research of matrix analysis and numerical algebra. We study bounds of the infinity norm of the inverse of Nekrasov matrices and obtain two new upper bounds which contain a parameter \(\varepsilon\). Numerical examples are given to illustrate that the estimates obtained using the upper bounds are more accurate than that using some existing upper bounds when the parameter \(\varepsilon\) is chosen appropriately.
MSC:
15A09 | Theory of matrix inversion and generalized inverses |
15A29 | Inverse problems in linear algebra |
15A60 | Norms of matrices, numerical range, applications of functional analysis to matrix theory |
65F35 | Numerical computation of matrix norms, conditioning, scaling |