MATH 475B Lecture Notes - Lecture 15: Homotopy
16 Mar 2016
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Page 1 of 7 - mar 10, 2011: how to get a good initial guess for newton: homotopy method, tricks for converting more general problems into bvps in standard form. For newtons method, you want to nd a root. If we have an initial guess x0, we can iterate, we need to be able to do this in a vector space that we can take derivatives in. It is possible with some work to estimate rho (p in above), (generally overestimate (conservative) in terms of ratios of rst and second derivatives of f(x). Usually the above is not practical, and it is easier and faster to just try newtons method. Page 2 of 7 - mar 10, 2011. Rho (p in above) is different for every region. If your initial guess is not close enough to root, results are completely unpredictable. Page 3 of 7 - mar 10, 2011.
