ChebyshevPolynomialsOnGrid

Evaluate Chebyshev polynomials and derivatives on an arbitrary grid.

Developer documentation: this item describes internal implementation details.

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Declaration

 [varargout] = ChebyshevPolynomialsOnGrid(x,N_polys)

Parameters

• x grid on which to evaluate the basis
• N_polys number of Chebyshev polynomials requested

Returns

• varargout basis matrices for the polynomials and requested derivatives

Discussion

          Chebyshev Polynomials on Grid   Compute the the first N Chebyshev polynomials and their derivatives for   an arbitrary grid x.

x_norm = ChebyshevPolynomialsOnGrid( x ) with exactly one argument, x, returns the x normalized to its typical [-1,1] values.

T = ChebyshevPolynomialsOnGrid( x, N_polys ) returns the first N_poly Chebyshev polynomials for an arbitrary grid x.

[T, T_x, T_xx,…] = ChebyshevPolynomialsOnGrid( x, N_polys ) returns the first N_poly Chebyshev polynomials and their derivatives for an arbitrary grid x.

The returned matrices T, T_xx, etc are size(T) = [length(x) N_polys], i.e., the polynomials are given column-wise.