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root finding uses refinement?
From: |
Ben Abbott |
Subject: |
root finding uses refinement? |
Date: |
Thu, 4 Oct 2007 08:37:50 -0400 |
I may have lost my mind, but I thought Octave used a script to
implement roots() ... perhaps this has recently changed?
In any event, I'd like to know if any root refinement is used by the
built-in function roots()?
I have an application in which small differences in roots can be
important. I'd like to improve the accuracy of the root finder so
that I may place a higher standard on pole multiplicity when finding
the residues of a quotient of polynomials (using 'residue')
I checked a simple polynomial ...
r = roots([1 0 18 0 81]) / 1i
r =
3.0000 + 0.0000i
-3.0000 + 0.0000i
3.0000 - 0.0000i
-3.0000 - 0.0000i
octave:20> r - round(r)
ans =
1.6920e-08 + 2.5814e-08i
-1.6920e-08 + 2.5814e-08i
-1.6920e-08 - 2.5814e-08i
1.6920e-08 - 2.5814e-08i
octave:21> eps
ans = 2.2204e-16
The error in the solution for the roots is about 8 orders of
magnitude larger than the numerical limit ... is this the simple
indicative of the present state of root finding or might a more
refinement method improve upon this?
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