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.

The "final exam" for this course will take place at 8:00 AM on Tuesday, 12 December. This will be an ordinary 50 minute test. It will be comprehensive, but weighted toward the latter half of the semester. As always, paper notes will be permitted, but no electronic devices will be allowed.

A Solution example is available for the quiz.

Assignment A is posted.

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