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From Connor Petty <mistercpp2...@gmail.com>
Subject [Math] MullerSolver2 does not respect initial bracketing
Date Sat, 12 Mar 2016 01:50:59 GMT
I've been doing some investigation regarding MATH-1333 and I cam across
some bounds issues in MullerSolver and MullerSolver2. There are a few test
cases I've created which cause these solvers to return values outside of
their initial bracket. I've created fixes for MullerSolver but
MullerSolver2 baffles me. MullerSolver is more or less an implementation of
the algorithm you can find at https://en.wikipedia.org/wiki/Muller's_method
while MullerSolver2 is an implementation of the algorithm at
http://mathworld.wolfram.com/MullersMethod.html. But the major difference
between MullerSolver 1 & 2 is that MullerSolver2 was designed to work
without bracketing. This turns out to make it fairly easy to make it return
faulty values.

Now my question is: How much should these solvers stick to their original
algorithms? If the original algorithm is flawed should solver exhibit those
same flaws?
There is some precedent for that in SecantSolver which has the same
guarantees of convergence as the original algorithm (which has none).
But MullerSolver2 is clearly a patched version of the algorithm it is based
off of and exhibits some very characteristic flaws from the original
algorithm. Should MullerSolver2's bounds issue be fixed or should that
issue just be accepted a limitation of that algorithm?

Best Regards,
Connor Petty

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