How to apply Taylor in this equation?

조회 수: 4 (최근 30일)
Aisha Mohamed
Aisha Mohamed . 2022년 9월 25일
편집: Torsten . 2022년 9월 26일
Hi all
I am really sorry because I have just now found (Bruno Luong answered your question what does the positive and negative values concave mean?.) (I do not know why I could not see it before now? maybe an error in my device).
The expert Bruno said,
((I'm bet you plot the colormap of cos(angle(P(z)) with P degree 2 and centered about z0 the root of P(z ).
A taylor expansion dz := z-z0 is
P(dz) = 0 + P'(z0)*dz + P''(z0)/2 * dz^2 .
So the phase of P(dz) make 2 turns when going around z0, so the cosine make 2 periods : you get 2 blues opposite and 2 yellows opposite. That's all normal and nothing to discover beside the fact that taylor expansion explains all that.)).
I understood from this answer and previuos answers from Torsten and David Goodmanson that the phase of P(dz) make 2 turns when going around z0. My questions are,
1-How to apply Taylor expansion in the case of this function
f_b(1/z) = (0.10 − 0.3i)z −1 + (0.2121 − 0.0008i)z −2 + (0.9 + 0.001i)z −3 and I wrote it in MATLAB as p1,
p1=[(0.9000 + 0.0010i) (0.2121 - 0.0008i) (0.1000 - 0.3000i) (0)] ;
when I plotted it I got
2-Does here the phase of P(dz) make 3 turns when going around z0,
3-what happened in the center of the figure(I put it inside circle ) , why the positive (yellow) and negative (blue) values overlap by this way?
I appreciate any help
  댓글 수: 2
Torsten 2022년 9월 26일
편집: Torsten 님. 2022년 9월 26일
Since this seems a private communication with Bruno Luong, you should ask him, not the forum.
We don't know the context of his remark.

댓글을 달려면 로그인하십시오.

답변 (0개)


Help CenterFile Exchange에서 Linear Algebra에 대해 자세히 알아보기


Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by