Unformatted text preview: α values produce small residuals for this problem. This is an inherent limitation in the problem and we cannot change it. It means, though, that we need to be very careful in computing and reporting results of exponential ±tting. One important requirement on the data is that there be a suﬃciently large number of points in the range where each of the exponential terms is large. CHALLENGE 13.3. When the true α = [ − . 3 , − . 4], the computations with 4 parameters produced unreliable results: [ − . 343125 , − 2 . 527345] for the ±rst guess and [ − . 335057 , − . 661983] for the second. The results for 2 parameters were somewhat better but still unreliable: [ − . 328577 , − . 503422] for the ±rst guess and [ − . 327283 , − . 488988] for the second. Note that all of the runs produced one signi±cant ±gure for the larger of the rate constants but had more trouble with the smaller. 75...
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 Fall '11
 Dr.Robin
 Exponential Function, Numerical Analysis, condition number, Sample Matlab Programs, ﬁrst guess, smallest singular value

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