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.

Assignment 6 is posted.

The midterm exam will take place on Friday, 12 October. As always, you are permitted any paper notes you find useful, but no electronic devices are allowed. The test is cumulative, but emphasizes the material covered in the last fours weeks. A sample exam is available.

You need to install Matlab on your computer by Wednesday. You do not need Simulink or any particular toolboxes, though you might find the Symbolic toolbox useful at some time in the future (not in this class).

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