1. a. Interpolate the function sin(x) at 5 Chebyshev points (using both Chebyshe

Question

1. a. Interpolate the function sin(x) at 5 Chebyshev points (using both Chebyshev-Gauss-Lobatto, and
Chebyshev-Gauss) over the interval [0; pi/2]. Compare your results to those you obtained in Homework 5
(using equispaced nodes).
b. Repeat (interpolate sin(x)), but this time use 5 Chebyshev points (using both Chebyshev-Gauss-Lobatto,
and Chebyshev-Gauss) over the interval [0;pi ]. What can you say?

2. Interpolate the Runge function
1/(1 + 25x^2) on the interval [-1; 1] using 10, 15, 20, and 25 equidistant points
and 10, 15, 20, and 25 Chebyshev points (using both Chebyshev-Gauss-Lobatto, and Chebyshev-Gauss).
Graph the interpolants.

Please provide only Matlab Code

Explanation / Answer

Please post as separate questions:

2)  Equally 11 spaced points of step size 1/5 and at the Chebyshev nodes.

>> f = @(x) (1./(1+25*x.^2));

>> xn=-1:.2:1; #Change step size here to change number of points between -1 and 1

>> yn=f(xn);

>> x=-1:.001:1;z=f(x);

>> plot(x,z,xn,yn,’o’)

The Interpolating polynomials plotted against the graph of f(x)

>> If=int_poly(yn,xn,x);

>> plot(x,z,x,If)

>> i=0:10;cn=cos(((2*i+1)./(22))*pi);

>> fcn=f(cn); >> Ifcn=int_poly(fcn,cn,x);

>> plot(x,z,x,Ifcn)

>> max(abs(z-Ifcn))

HOPE IT HELPS!

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