Theory and Modern Applications
Table 2 Maximum absolute errors of problem ( 65 )
N = M | \(\boldsymbol{\alpha }_{\boldsymbol{1}}\boldsymbol{=}\boldsymbol{\beta }_{\boldsymbol{1}}\boldsymbol{=}\boldsymbol{\alpha }_{\boldsymbol{2}}\boldsymbol{=}\boldsymbol{\beta }_{\boldsymbol{2}}\boldsymbol{=}\boldsymbol{-\frac{1}{2}}\) | \(\boldsymbol{\alpha }_{\boldsymbol{1}}\boldsymbol{=}\boldsymbol{\beta }_{\boldsymbol{1}}\boldsymbol{=}\boldsymbol{\alpha }_{\boldsymbol{2}}\boldsymbol{=}\boldsymbol{\beta }_{\boldsymbol{2}}\boldsymbol{=}\boldsymbol{\frac{1}{2}}\) | \(\boldsymbol{\alpha }_{\boldsymbol{1}}\boldsymbol{=}\boldsymbol{\beta }_{\boldsymbol{1}}\boldsymbol{=}\boldsymbol{\frac{1}{2}}\) , \(\boldsymbol{\alpha }_{\boldsymbol{2}}\boldsymbol{=}\boldsymbol{\beta }_{\boldsymbol{2}}\boldsymbol{=}\boldsymbol{-\frac{1}{2}}\) | |||
|---|---|---|---|---|---|---|
\(\boldsymbol{M}_{\boldsymbol{1}}\) | \(\boldsymbol{M}_{\boldsymbol{2}}\) | \(\boldsymbol{M}_{\boldsymbol{1}}\) | \(\boldsymbol{M}_{\boldsymbol{2}}\) | \(\boldsymbol{M}_{\boldsymbol{1}}\) | \(\boldsymbol{M}_{\boldsymbol{2}}\) | |
4 | 2.20 × 10−3 | 2.64 × 10−3 | 2.14 × 10−3 | 2.43 × 10−3 | 2.13 × 10−2 | 2.46 × 10−3 |
8 | 7.64 × 10−8 | 7.48 × 10−8 | 1.29 × 10−7 | 1.24 × 10−7 | 4.33 × 10−8 | 3.87 × 10−8 |
12 | 3.81 × 10−13 | 3.77 × 10−13 | 9.46 × 10−13 | 9.46 × 10−13 | 4.32 × 10−13 | 4.40 × 10−13 |
16 | 5.50 × 10−15 | 4.101 × 10−15 | 3.69 × 10−15 | 3.44 × 10−15 | 2.33 × 10−15 | 2.33 × 10−15 |
20 | 3.66 × 10−15 | 3.66 × 10−15 | 9.83 × 10−15 | 7.22 × 10−15 | 2.33 × 10−15 | 2.33 × 10−15 |