AngouriMath
SameRootTolerance
Field
Summary
How far apart two candidates may be, relative to their own size, and still be
the same root.
the same root.
Remarks
The search starts from a grid and iterates in double precision, so the same root
reached from different starting points comes back agreeing to about sixteen
significant digits and differing after that. Left as they were, those were
counted as separate answers: x^5 + 3x + 1 came back with 28 roots and x^6 + x + 1
with 23, four of the 28 being -0.83907243306660750, -0.83907243306660761,
-0.83907243306660773 and -0.83907243306660784.
The measured room is wide. Candidates for one root lie within 1e-15 of each other
relative to their size, while the nearest two distinct roots over the twelve
polynomials tried are 0.42 apart. This is 1e-13: a hundred times above the noise
and still twelve orders below the closest two roots that were ever told apart.
reached from different starting points comes back agreeing to about sixteen
significant digits and differing after that. Left as they were, those were
counted as separate answers: x^5 + 3x + 1 came back with 28 roots and x^6 + x + 1
with 23, four of the 28 being -0.83907243306660750, -0.83907243306660761,
-0.83907243306660773 and -0.83907243306660784.
The measured room is wide. Candidates for one root lie within 1e-15 of each other
relative to their size, while the nearest two distinct roots over the twelve
polynomials tried are 0.42 apart. This is 1e-13: a hundred times above the noise
and still twelve orders below the closest two roots that were ever told apart.
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