Hi.
On Fri, 11 Mar 2016 17:50:59 -0800, Connor Petty wrote:
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?
Fully.
Or the name and documentation of the class must clearly reflect that
it is a variation.
If the original algorithm is flawed should solver exhibit those
same flaws?
Yes (if the flaw is in the algorithm itself, not just in the
implementation,
e.g. because the expected properties assume infinite precision).
But whenever possible the implementation should (_must_, IMHO) check
that
it has not hit one of its own limitation, and "fail early".
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
Do you have the possibility to check another implementation of that
algorithm?
Since the Javadoc says that the original deals with complex values but
CM
avoids it, I wonder whether this could be the problem.
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?
Cf. above.
Best regards,
Gilles
Best Regards,
Connor Petty
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