Department of Mathematics

Math 300: Mathematical Computing

ICE: Matlab Flow

Recall that the three-term recurrence relation for Chebyshev polynomials is given by \[ T_{k+1}(x) = 2xT_k(x)-T_{k-1}(x), \] where we know that \(T_0(x) = 1,\) and \(T_1(x)=x,\) for \(x\in[-1,1].\) Given some maximal degree \(K\) that we choose, write a script that uses this relation to generate a \((K+1)\times N\) array T whose \(k^\text{th}\) row comprises the values of \(T_{k-1}\) at some vector \(x\) of length \(N\), which you provide. In other words, T(k+1,n)\(=T_k(x_n)\) for \(k=0,1,\dots,K\) and \(n=1,2,\dots,N\). Your script should then plot the rows of T.

A solution for the final is available.

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