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Computing a rotation in interval arithmetic can lose tightness. Instead of computing a cos phi + b sin phi which doesn't account for the difference in phase in the two sinusoids, it is better to use sqrt (a² + b²) * cos ( phi - atan2(a,b) ) which correctly estimates the maximum amplitude of the sum to be sqrt(a²+b²) instead of abs(a) + abs(b). This seems to worsen the performance of the interval Newton method at the moment, possibly due to the complexity of the new formula, which involves computing atan(b/a). Further investigation is needed. |
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| installation_notes.md | ||
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