AngouriMath
DurandKerner
Description
Summary
Every root of a square-free polynomial with whole coefficients, to the working precision,
by the Durand–Kerner iteration: each approximation moves byp(z_i) / prod_{j != i}
(z_i - z_j) , which is Newton's step for the root it is nearest once the others are
close to theirs, so the iteration converges to all the roots at once and quadratically at
the end.
by the Durand–Kerner iteration: each approximation moves by
(z_i - z_j)
close to theirs, so the iteration converges to all the roots at once and quadratically at
the end.
Remarks
answer, so where the iteration does not settle, or settles on two approximations too close
to tell apart, there is no answer. A square-free polynomial has no repeated root, so two
approximations that close mean the iteration has not separated them.
imaginary part is smaller than half the separation that was checked is real: were it not,
it and its conjugate would be closer together than that. It is written as a real number
then, rather than as one with an imaginary part of
Members
GuardDigits
FieldMaxSweeps
FieldRoots(AngouriMath.Functions.IntegerPolynomial,PeterO.Numbers.EContext)
Method
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