MATH307 April 2012
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Question 05 (b)
You are given a set of 100 data points (xn, yn) with xn increasing.
(b) Write down the matrix equation that is satisfied by the coefficients of this polynomial. Is the numerical solution of this equation likely to be accurate, and why?
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From part (a), we know that we require a polynomial of degree 99, of the form:
Since for , then there are 100 linear equations for the coefficient vector
Therefore, the matrix equation that is satisfied is:
However, since the Vandermonde matrix not very well conditioned (because Vandermonde matrices have large condition numbers, an error in the data points can cause a relatively large error in the solution), it is unlikely that the solution is accurate
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