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chebpol

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Generates the Chebyshev polynomials of the first kind. This command can be used in combination with dcht to calculate the Chebyshev interpolation. Compared to the chebin command, using chebpol for the interpolation offers additional control over the interpolation process as it allows the user to specify the polynomial order.

 

Supported Product: FDTD, MODE

 

Syntax

Description

chebpol(N,xi,xmin,xmax)

This command generates a matrix containing the Chebyshev polynomials of the first kind of orders zero to N-1 evaluated at the xi points.

 

Example

This example uses chebpol to interpolate function f and compares the results to the original points.

clear;

closeall;

 

# Sample function on Chebyshev grid 

 

xmin = 0.0;

xmax = 1.0;

Nc = 11;

x = chpts(xmin,xmax,Nc);

f = cos(2.0*pi*x)+1i*sin(2.0*pi*x); 

Ni = 100;

xi = linspace(xmin,xmax,Ni);

 

# Chebyshev interpolation done by hand

 

dchtf = dcht(f);

Tx = chebpol(length(f),xi,xmin,xmax);

fi = mult(Tx,dchtf);

 

plot(xi,fi,"x","f(x)","Function Interpolated by Hand");

holdon;

plot(x,f,"x","f(x)","Function Interpolated by Hand","plot points");

holdoff;

legend("Re - Interpolated","Im - Interpolated","Re - Exact","Im - Exact");

setplot("y1 max",1.05);

setplot("y1 min",-1.05);

setplot("y2 max",1.05);

setplot("y2 min",-1.05);

 

See Also

dcht,chpts,icht,chebin,chebpol1

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