09/10/2007, 05:22 PM
By the way, if you're wondering about the periodicity to the graph (which resembles the periodicity of the root test graphs), the explanation is simple. There are errors in both the magnitude and phase (complex rotation) of the terms, and these errors diminsh with increasing matrix size.
The errors in magnitude should be fairly stable, but the errors in phase will be magnified when the real part is approaching 0. The explanation is easier to understand if we look strictly at the cosine function (which gives us the real part).
\( \cos(1.5 + \epsilon) \) has a greater absolute error than \( \cos(\epsilon) \). If you then divide by the expected result, the errors are magnified further, because 1 divided by \( \cos(1.5 + \epsilon) \) is about 14.
The errors in magnitude should be fairly stable, but the errors in phase will be magnified when the real part is approaching 0. The explanation is easier to understand if we look strictly at the cosine function (which gives us the real part).
\( \cos(1.5 + \epsilon) \) has a greater absolute error than \( \cos(\epsilon) \). If you then divide by the expected result, the errors are magnified further, because 1 divided by \( \cos(1.5 + \epsilon) \) is about 14.
~ Jay Daniel Fox