AngouriMath
RootsEnclosed(AngouriMath.Entity,AngouriMath.Entity.Variable)
Method (no overloads)
Summary
A rectangle about each root of polynomial in w ,
holding that root and no other; null where the polynomial does not have rational
coefficients, or the rectangles cannot be kept apart.
holding that root and no other; null where the polynomial does not have rational
coefficients, or the rectangles cannot be kept apart.
Remarks
Durand–Kerner's approximations z_k at this precision, each enclosed by its
Weierstrass correctionw_k = p(z_k)/(a prod_{j != k} (z_k - z_j)) , worked out in
intervals. Every root lies in a disk about somez_k - w_k of radius
(n - 1)|w_k| , and a disk apart from the others holds exactly one (Braess and
Hadeler). That disk is inside the one of radiusn|w_k| about z_k , whose
square is the rectangle, so rectangles apart from each other hold one root each.
Weierstrass correction
intervals. Every root lies in a disk about some
Hadeler). That disk is inside the one of radius
square is the rectangle, so rectangles apart from each other hold one root each.
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