Chebychev Division Approximation at low degrees

Library Questions
1

Hi,

I was playing around with the EvalDivide() function at different polynomial degrees and wanted to confirm whether my results are expected or whether I’m doing something wrong:

grafik
grafik1653×747 76 KB

The green line is the baseline of what the division result of 1/x is in plaintext. The blue line shows the approximation result with different degrees.
(The red line is irrelevant for this post)

I am aware that the results of the approximation will not be accurate at lower degrees. I was surprised by the fact that the results change between being bigger and smaller than the real result until it settles at some point.
Is this expected behavior?

Thanks!
Clemens

2

This behavior is specific to Chebyshev series interpolation. You will observe the same effect if you play with a plaintext version of Chebyshev interpolation.