Wolfram Function Repository
Instant-use add-on functions for the Wolfram Language
Function Repository Resource:
Produce Chebyshev nodes
ResourceFunction["ChebyshevNodes"][n] produces n Chebyshev nodes in the range from -1 to 1. | |
ResourceFunction["ChebyshevNodes"][n,{min,max}] produces n Chebyshev nodes in the domain min to max. |
Create ten Chebyshev nodes analytically:
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Approximate the numbers:
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Create the numbers on a domain from 0 to 2π:
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Show on a number line:
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Find points for fifth order approximation:
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Perform the approximation of Cos[x]:
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Represent the approximation as a polynomial:
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Compare the functions:
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Show the difference:
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Compare to the error from a fifth-order series expansion evaluated at the midpoint:
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The Chebyshev nodes are related to the roots of Chebyshev polynomials of the first kind:
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Compare the zeros by finding the roots numerically and using the function ChebyshevNodes:
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Chebyshev nodes match the coordinate components of CirclePoints:
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Show how Chebyshev nodes are related to equi-distantly spaced points on a semi-circle:
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Wolfram Language 13.0 (December 2021) or above
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