Table 4 Residual and CPU time in seconds for solving Example 3.4 by four methods for different sizes.
n | Back-slash | QR | LU | Our Algorithm 1 | Our Algorithm 2 | |||||
|---|---|---|---|---|---|---|---|---|---|---|
RES | Time (s) | RES | Time (s) | RES | Time (s) | RES | Time (s) | RES | Time(s) | |
\(2^{10}\) | 3.2196e−15 | 0.0210 | 3.2196e−15 | 0.0168 | 5.6621e−15 | 0.0591 | 2.8866e−15 | 0.0098 | 4.1078e−15 | 0.0091 |
\(2^{11}\) | 4.3299e−15 | 0.1247 | 4.3299e−15 | 0.1016 | 5.6621e−15 | 0.4107 | 4.9960e−15 | 0.0122 | 4.9960e−15 | 0.0112 |
\(2^{12}\) | 6.1062e−15 | 0.7124 | 6.1062e−15 | 0.5967 | 9.6589e−15 | 2.7468 | 5.5511e−15 | 0.0360 | 5.5511e−15 | 0.0271 |
\(2^{13}\) | 1.0325e−14 | 4.7019 | 1.0325e−14 | 4.4022 | 1.3434e−14 | 21.0452 | 4.8295e−15 | 0.0538 | 4.8850e−15 | 0.0397 |
\(2^{14}\) | 1.2879e−14 | 33.5569 | 1.2879e−14 | 33.3971 | 2.9643e−14 | 166.9035 | 3.9413e−15 | 0.1067 | 3.9302e−15 | 0.0700 |