Orthogonal Polynomial Series in Numpy: Playing with Legendre and Chebyshev Series

[@jiabeiba]

Thanks, Kevin for the explanation on Chebyshev. It cleared some of my doubts. I will go through the video again.

[@holyshit922]

I played with them three ways
1) using recurrence relation
2) using ordinary differential equation
3) by orthogonalisation of basis {1,x,x^2,...,x^n} with inner product

[@edmonda.9748]

Thanks for clear explanation
Is there a an inverse command in python for chebyshev transform?,
I mean, when you have the chebyshev coefficients and want to find the original time series.
Thanks

[@kpmooney]

Not that I know of. You'd have to define inverse transform in terms of cosine transforms.

[@pedrofernandez5410]

Thank you for the video. I am having an issue when I am applying Legendre model to my data set. I use legfit to get the coefficients for a legendre series that overfits my data quite well but when I attempt to expand my x data set (to interpolate more y data), my legendre model does not nicely fit my expanded data set and instead almost oscillates with every step size. I am not sure why this is happening. Any suggestions?

[@kpmooney]

It's hard to diagnose whiteout seeing the code and data, but it sounds like over fitting. Remember, an Nth order polynomial will generally have n-1 wiggles.