Table 1 Residual and CPU time in seconds for solving Example 3.1 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) | |
\(2^{10}\) | 2.3315e−15 | 0.0170 | 2.3315e−15 | 0.0155 | 5.8842e−15 | 0.0732 | 3.0254e−15 | 0.0065 | 2.6923e−15 | 0.0084 |
\(2^{11}\) | 3.4417e−15 | 0.1245 | 3.4417e−15 | 0.0965 | 7.1054e−15 | 0.4303 | 6.8834e−15 | 0.0094 | 6.9944e−15 | 0.0123 |
\(2^{12}\) | 5.7732e−15 | 0.7712 | 5.7732e−15 | 0.5901 | 1.2546e−14 | 3.0541 | 4.5519e−15 | 0.0192 | 4.4409e−15 | 0.0253 |
\(2^{13}\) | 9.5479e−15 | 5.0455 | 1.0325e−14 | 4.4950 | 2.4536e−14 | 23.0388 | 9.4411e−14 | 0.0419 | 9.4050e−14 | 0.0466 |
\(2^{14}\) | 1.2990e−14 | 34.5136 | 1.2990e−14 | 34.6899 | 3.4195e−14 | 172.4416 | 7.3497e−14 | 0.0637 | 7.3275e−14 | 0.0698 |