Functions

Vector of relative errors of P at the points X

alpha, beta quantities for Newton convergence to an approximate zero.

• If alpha < 0.125, then the approximate zero is within 2*beta from Xi and Newton methods converges to it from Xi quadratically.
• If alpha < 0.02, then Newton method converges from all points in the ball of center Xi and radius 2*beta.

newton_improve!(Xi::Matrix, P, X=variables(P), eps::Float64=1.e-12, Nit::Int64 = 20)

Improve the roots Xi of the system P by Newton iteration.

• Xi matrix of n x r roots where n is the number of coordinates of the roots and r the number of roots
• P is the (square) system of polynomials
• X the array of variables
• eps threshold for stoping the iteration when the relative error is smaller.
• Nit is the maximal number of iterations per root.