Table 1 The upper bounds for \(\|A_{i}^{-1}\|_{\infty }\), \(i=1,2,3\)
From: An improvement of the infinity norm bound for the inverse of \(\{P_{1},P_{2}\}\)-Nekrasov matrices
Matrix | Exact \(\|A_{i}^{-1}\|_{\infty }\) | Varah’s bound | \(\{P_{1},P_{2}\}\)-Nek I | \(\{P_{1},P_{2}\}\)-Nek II | Bound (9) |
|---|---|---|---|---|---|
\(A_{1}\) | 0.1796 | 0.5000 | 0.2132 | 0.2433 | 0.1869 |
\(A_{2}\) | 0.3455 | – | 0.7726 | 0.5992 | 0.5989 |
\(A_{3}\) | 1.0578 | – | 1.1140 | 1.1255 | 1.0646 |