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NumericalCertification :: newtonOper

newtonOper -- apply Newton's method on a given point.

Synopsis

Description

This function applies Newton's method on a given point and given polynomial system.

It converges to an exact solution if a given point is an approximate solution.

i1 : R = QQ[x1,x2,y1,y2];
i2 : f = polySystem {3*y1 + 2*y2 -1, 3*x1 + 2*x2 -7/2,x1^2 + y1^2 -1, x2^2 + y2^2 - 1};
i3 : p = point{{.95,.32,-.30,.95}};
i4 : newtonOper(f,p)

o4 = {.954379, .318431, -.298633, .947949}

o4 : Point

However, if the Jacobian of the system is singular at the point, it just returns the input.

i5 : p = point{{0,.32,0,.95}};
i6 : newtonOper(f,p)

o6 = p

o6 : Point

Ways to use newtonOper :

For the programmer

The object newtonOper is a method function.