Theory and Modern Applications
\(r = \frac{2-\beta }{\beta }\) | n = 32 | n = 64 | n = 128 | n = 256 | n = 512 | n = 1028 | |
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β = 0.2 | \(E_{\mathrm{max}_{I}}^{n}\) | 1.733E−2 | 5.046E−3 | 1.455E−3 | 4.183E−4 | 1.202E−4 | 3.451E−5 |
\(\text{rate}_{E_{\mathrm{max}_{I}}^{n}}\) | 1.780 | 1.794 | 1.798 | 1.800 | 1.800 | Â | |
\(E_{\mathrm{max}}^{n}\) | 5.105E−2 | 2.580E−2 | 1.279E−2 | 6.399E−3 | 3.188E−3 | 1.598E−3 | |
\(\text{rate}_{{E_{\mathrm{max}}^{n}}}\) | 0.984 | 1.012 | 1.000 | 1.005 | 0.996 | Â | |
\(\text{rate}_{E_{\mathrm{conv}}^{n}}\) | 1.083 | 1.058 | 1.004 | 1.039 | 1.052 | Â | |
β = 0.4 | \(E_{\mathrm{max}_{I}}^{n}\) | 3.239E−2 | 1.096E−2 | 3.645E−3 | 1.206E−3 | 3.982E−4 | 1.314E−4 |
\(\text{rate}_{E_{\mathrm{max}_{I}}^{n}}\) | 1.564 | 1.588 | 1.596 | 1.599 | 1.600 | Â | |
\(E_{\mathrm{max}}^{n}\) | 4.603E−2 | 2.310E−2 | 1.157E−2 | 5.786E−3 | 2.892E−3 | 1.444E−3 | |
\(\text{rate}_{{E_{\mathrm{max}}^{n}}}\) | 0.995 | 0.998 | 0.999 | 1.001 | 1.002 | Â | |
\(\text{rate}_{E_{\mathrm{conv}}^{n}}\) | 1.060 | 1.043 | 1.030 | 1.022 | 1.018 | Â | |
β = 0.6 | \(E_{\mathrm{max}_{I}}^{n}\) | 6.202E−2 | 2.460E−2 | 9.487E−3 | 3.619E−3 | 1.375E−3 | 5.216E−4 |
\(\text{rate}_{E_{\mathrm{max}_{I}}^{n}}\) | 1.334 | 1.374 | 1.390 | 1.396 | 1.399 | Â | |
\(E_{\mathrm{max}}^{n}\) | 6.202E−2 | 2.460E−2 | 1.028E−2 | 5.141E−3 | 2.568E−3 | 1.282E−3 | |
\(\text{rate}_{{E_{\mathrm{max}}^{n}}}\) | 1.334 | 1.258 | 1.000 | 1.001 | 1.003 | Â | |
\(\text{rate}_{E_{\mathrm{conv}}^{n}}\) | 1.059 | 1.051 | 1.043 | 1.036 | 1.031 | Â | |
β = 0.8 | \(E_{\mathrm{max}_{I}}^{n}\) | 1.201E−1 | 5.673E−2 | 2.563E−2 | 1.134E−2 | 4.974E−3 | 2.172E−3 |
\(\text{rate}_{E_{\mathrm{max}_{I}}^{n}}\) | 1.082 | 1.146 | 1.176 | 1.189 | 1.195 | Â | |
\(E_{\mathrm{max}}^{n}\) | 1.201E−1 | 5.673E−2 | 2.563E−2 | 1.134E−2 | 4.974E−3 | 2.172E−3 | |
\(\text{rate}_{{E_{\mathrm{max}}^{n}}}\) | 1.082 | 1.146 | 1.176 | 1.189 | 1.195 | Â | |
\(\text{rate}_{E_{\mathrm{conv}}^{n}}\) | 1.384 | 1.444 | 1.256 | 1.037 | 1.038 | Â |