Table 2 Residual and CPU time in seconds for solving Example 3.2 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) | |
\(2^{10}\) | 6.6613e−16 | 0.0235 | 6.6613e−16 | 0.0215 | 4.3299e−15 | 0.3554 | 4.3299e−15 | 0.0084 | 4.1078e−15 | 0.0065 |
\(2^{11}\) | 5.5511e−16 | 0.1272 | 5.5511e−16 | 0.0995 | 1.2212e−15 | 1.3883 | 4.4964e−15 | 0.0132 | 4.2744e−15 | 0.0096 |
\(2^{12}\) | 7.7716e−16 | 0.6192 | 7.7716e−16 | 0.5956 | 1.3323e−15 | 5.5822 | 4.2744e−15 | 0.0288 | 4.2188e−15 | 0.0244 |
\(2^{13}\) | 6.6613e−16 | 4.7716 | 6.6613e−16 | 4.2961 | 4.1078e−15 | 27.7111 | 4.1078e−15 | 0.0576 | 4.2188e−15 | 0.0466 |
\(2^{14}\) | 7.7716e−16 | 33.2503 | 7.7716e−16 | 32.6906 | 1.6653e−15 | 185.3402 | 1.2212e−14 | 0.1109 | 1.2323e−14 | 0.0682 |