• Lesson Plan
• 66

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– 20 – Many observers use the 3 σ criterion: discard any points with residuals exceeding 3 σ . This is definitely not a good idea: the limit 3 σ is Chauvenet’s criterion for M = 185 datapoints. Very often M exceeds this, often by a lot. To apply Chauvenet’s criterion it’s most convenient to calculate the inverse error function. For this, you have two choices. One (for sissies like myself), you can use inverf.pro from my area heiles/idl/gen . But the real he-man will want to learn about using a root-finding algorithm such as Newton’s method (NR § 9.4 and 9.6) together with the error function; both procedures exist in IDL as newton and errorf . You at least ought to skim lightly some of NR’s chapter 9 about root finding, because some day you’ll need it. 7. NONLINEAR LEAST SQUARES The least-squares formulation requires that the data values depend linearly on the unknown coefficients. For example, in equation 0.1, the unknown coefficients A and B enter linearly. Suppose you have a nonlinear dependence, such as wanting to solve for A and B with equations of condition that look like sin( At m ) + Bt m = y m . (7.1) What do you do here? You linearize the process, using the following procedure.
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