If x = 0:.1:1, (so that n = 10) what scaling factor h gives the smallest conditi

Question

If x = 0:.1:1, (so that n = 10) what scaling factor h gives the smallest condition number of the Vandermonde matrix interpolating at the points in h*x? You are to investigate this numerically; use the standard Matlab cond(A) (which uses the Euclidean norm) for calculating the condition number. Use the following logarithmic scale for h, in which log(h) has uniform increments: h=2.^(-1:.05:2). i) Calculate the condition number C for each value of h and then make a plot of log(C) against log(h). ii) Why is it a good idea to plot log(C) rather than just C? iii) What value of h, approximately, gives the smallest condition number? And what is that condition number, approximately?

Explanation / Answer

For the second question:

plotting log(c) is good idea rather plotting just c.

Log of a quantity encompases wider range of values and provides better visibility in results.

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