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Python code for Fake Nodes interpolation approach.

License: GNU General Public License v3.0

Python 0.19% Jupyter Notebook 99.81%

fakenodes's Introduction

Hi there ๐Ÿ‘‹

my face

I am Davide Poggiali. Italian guy, DataScientist, formerly a PostDoc. Mathematician, PhD in Neuroscience.

[MRI,CT,PET,SPECT]-neuroimager ๐Ÿง 

Numerical Analyst ๐Ÿ“ˆ

pythonist ๐Ÿ,

bike-faithful ๐Ÿšฒ,

guitarist ๐ŸŽธ.

See my website for other info.

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fakenodes's Issues

Great Idea!

The FakeNode approach is a great idea! A lot of engineering and math is based on interpolating polynomials. I work with ODE's a lot. Specifically, I work with stiff ODE's. I am wondering if given constant step size, can the BDF formulas be extended to higher than 7th order. Also, calculating numerical derivatives may converge better using this approach since the underlying function approximation is improved because of the FakeNode approach.

Thank you for posting your FakeNodes repo!

what is the math behind "lagrange(x, xx)" function?

Hi,

Could you say a few words about the math behind the function lagrange(x, xx).
In particular, "np.prod(np.matlib.repmat(xx.reshape(m,1),1,n-1) - np.matlib.repmat(x_k,m,1) , axis=1)".

Besides, the return value of "largange(x, xx)" is the reverse of a Vandermonde matrix, am I right?

Thanks a lot.

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