Table 3 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 | 7.93 × 101 | 8.25 × 102 | 3.80 × 106 |
10−1 | 4.26 × 102 | 6.69 × 102 | 4.97 × 105 |
10−2 | 2.31 × 103 | 4.37 × 102 | 1.67 × 105 |
10−3 | 1.28 × 104 | 7.74 × 102 | 1.62 × 105 |
10−4 | 7.25 × 104 | 1.29 × 103 | 1.69 × 105 |
10−5 | 4.12 × 105 | 1.39 × 103 | 1.71 × 105 |
10−6 | 2.23 × 106 | 1.40 × 103 | 1.72 × 105 |
10−7 | 7.81 × 106 | 1.40 × 103 | 1.72 × 105 |
10−8 | 1.20 × 107 | 1.40 × 103 | 1.72 × 105 |
10−9 | 1.28 × 107 | 1.40 × 103 | 1.72 × 105 |
10−10…10−12 | 1.29 × 107 | 1.40 × 103 | 1.72 × 105 |