increasing the precision of finding roots of a polynomial in matlab

Question

我有一个多项式取决于matlab中的x和y ，当我发现它的根是不同的x ，有时多项式中的根的替换值几乎不是零，这是什么问题？

Answer 1

Numerical issues may arise when x and y are poorly scaled. If, for example, your root (x,y) has very large values, machine precision might prevent you from getting the precise root. Try scale your function to a compact domain around (0,0) (usually [-1,1]x[-1,1] is a good starting point).

%// let mx and my be upper bounds to |x| and |y| respectively
nx = x / mx; %// change of variables
ny = y / my;
%// express your polynom in nx and ny and solve for them
%// let nrx and nry be a root of the polynom in the new changed variables, then:
rx = nrx * mx; %// root in original varialbes
ry = nry * my;
%// if you want to verify that the roots indeed brings your polynom to zero, you should try it in the scaled domain with rnx, rny.