Chebishev polynomials, don't know how to use "chebpoly"

10 views (last 30 days)
I wrote the following code to approximate a 2 variables function:
clear
clc
close all
FlowMeasurements = chebpts(5,[-0.2,0.8]); % mass flow Chebyshev
SpeedMeasurements = chebpts(5,[25000, 55000]); %Rotational speed Chebyshev
CompressorMapMatrix =[
1.5805 1.2092 1.1402 1.0234 1.0095
1.6553 1.2840 1.2564 1.0565 1.0287
1.9070 1.5357 1.7124 1.2518 1.1505
2.2873 1.9160 2.4317 1.7374 1.4732
2.4935 2.1222 2.8189 2.0728 1.7064]; % I put the points Chebishev will ask
FlowVector = -0.2:0.01:0.8;
approximationResult = chebfun2(CompressorMapMatrix,[ -0.2 0.8 25000 55000]);
a = chebcoeffs2(approximationResult); %a_ij Matrix
for i=1:length(SpeedMeasurements)
figure(2)
plot(approximationResult(FlowVector, SpeedMeasurements(i)));
hold on
grid on
end
Now I have to write this equation:
I have the a_ij Matrix, but I don't know how to get the:
I know for sure I have to use chebpoly but I don't know how.
This maybe could help:
https://www.chebfun.org/docs/guide/guide04.html

Answers (2)

Paul Rogers
Paul Rogers on 14 May 2020
maybe this can help
By Chebyshev points we shall mean the set of points in [1,1] defined by
xj=cos(jπ/N), 0jN,
where N1 is an integer. (If N=0, we take x0=0.) A fuller name is that these are Chebyshev points of the second kind. (Chebfun also enables computations based on Chebyshev points of the first kind; see Section 8.9.) Through any data values fj at these points there is a unique polynomial interpolant p(x) of degree N, which we call the Chebyshev interpolant. In particular, if the data are fj=(1)nj, then p(x) is TN(x), the degree N Chebyshev polynomial, which can also be defined by the formula TN(x)=cos(Ncos1(x)). In Chebfun, the command chebpoly(N) returns a chebfun corresponding to TN, and poly returns coefficients in the monomial basis 1,x,x2,. Thus we can print the coefficients of the first few Chebyshev polynomials like this:
taken from here

Paul Rogers
Paul Rogers on 17 May 2020
Can anyone help me on how to find T_i and T_j?

Categories

Find more on Polynomials in Help Center and File Exchange

Tags

Products


Release

R2014b

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!