Chebyshev Polynomials | Theory & Practice

Today I discuss what are Chebyshev polynomials and why we need them. After Introducing Chebyshev polynomials and their properties, I will write three separate codes to generate Chebyshev polynomials in MATLAB.

Chebyshev nodes can help us interpolate functions. They are much better than linearly spaced nodes. In the video I explain why Chebyshev nodes are a better option, and provide an example to show that equally spaced nodes may lead to a wrong result.

Watch the video and tell me what you think in the comments.

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Link to other tutorials mentioned in this video:

Proof for Chebyshev Polynomials recursion relation:

♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦
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0:00 - Introduction to Chebyshev Polynomials
00:40 - Chebyshev Polynomials in MATLAB
02:40 - Using Chebyshev Polynomials to Interpolate Functions
04:48 - Chebyshev Interpolation vs Equally Spaced Interpolation
06:43 - Changing Chebyshev Interpolation Interval
07:34 - Chebyshev Approximation
08:00 - Chebyshev Polynomials Orthogonality

Calculus
Numbers
Polynomials
Algebra
Mathematics
math
maths
Chebyshev
Chebyshev Polynomials
Chebyshev Polynomials in MATLAB
MATLAB Chebyshev Polynomials
Chebyshev Approximation
Chebyshev Polynomials Orthogonality

#calculus #polynomials #mathematics

[justinsostre]

The reason your recursion is slow is because you used a naive approach instead of, perhaps, tail recursion.