Table 2 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 | 1.47 × 102 | 3.67 × 101 | 6.27 × 106 |
10−1 | 1.12 × 103 | 7.27 × 101 | 8.17 × 105 |
10−2 | 3.95 × 103 | 6.46 × 101 | 2.75 × 105 |
10−3 | 2.94 × 104 | 1.24 × 102 | 2.78 × 105 |
10−4 | 6.30 × 104 | 2.07 × 102 | 1.87 × 105 |
10−5 | 6.41 × 104 | 2.03 × 102 | 1.57 × 105 |
10−6 | 6.41 × 104 | 2.03 × 102 | 1.55 × 105 |
10−7…10−12 | 6.41 × 104 | 2.03 × 102 | 1.54 × 105 |