Table 1 The condition numbers of the stiffness matrices for \(\pmb{n=9}\)
From: A diagonal preconditioner for singularly perturbed problems
ϵ | \(\boldsymbol{\operatorname{cond}(\mathbf{D}_{n}^{S} \mathbf{A}_{n} \mathbf{D}_{n}^{S})}\) | \(\boldsymbol{\operatorname{cond}(\mathbf{D}_{n}^{\mathrm{new}} \mathbf{A}_{n} \mathbf{D}_{n}^{\mathrm{new}})}\) | \(\boldsymbol{\operatorname{cond}(\mathbf{A}_{n})}\) |
|---|---|---|---|
10−0 | 2.69 × 101 | 1.45 × 102 | 2.67 × 106 |
10−1 | 7.40 × 101 | 1.32 × 102 | 3.31 × 105 |
10−2 | 2.20 × 102 | 7.07 × 101 | 1.10 × 105 |
10−3 | 6.68 × 102 | 1.66 × 102 | 1.11 × 105 |
10−4 | 1.23 × 103 | 3.31 × 102 | 1.18 × 105 |
10−5 | 1.37 × 103 | 3.72 × 102 | 1.22 × 105 |
10−6 | 1.39 × 103 | 3.77 × 102 | 1.22 × 105 |
10−7…10−12 | 1.39 × 103 | 3.78 × 102 | 1.23 × 105 |