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AngouriMath.Functions.Algebra.NumericalSolving

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Classes within the AngouriMath.Functions.Algebra.NumericalSolving namespace

• DurandKerner

  Summary

  Every root of a square-free polynomial with whole coefficients, to the working precision,
  by the Durand–Kerner iteration: each approximation moves by p(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.
  

  Remarks

  All the roots or none: a sum over the roots of a polynomial that is missing one is a wrong
  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.
  The coefficients are real, so the non-real roots come in conjugate pairs, and a root whose
  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 1e-110 that no root has.
  #1285

• NewtonSolver