matlab - 提高matlab中多项式求根的精度

Question

我有一个多项式取决于x和y在matlab中，当我找到它的不同根时x，有时多项式中根的替换不是几乎为零的值，有什么问题？

Answer 1

当缩放比例不佳时x，可能会出现数值问题。y例如，如果您的根(x,y)具有非常大的值，则机器精度可能会阻止您获得精确的根。尝试将您的功能扩展到一个紧凑的域(0,0)（通常[-1,1]x[-1,1]是一个很好的起点）。

%// 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.