polynomial multiplication not accurate, using conv() vs symbolic

I'm calculating the square of a polynomial inside a loop. It seems to me that, calculating it using conv() is resulting in large errors, compared to converting the polynomial to symbolic and do the calculation there.

Just out of curiosity, I tried to sym2poly the symbolic results back to polynomial, and the error appears again.

However, I can't using symbolic calculation in the loop, because it's too slow.

Any input on why this is happening and how to solve it properly? Thanks in advance.

figure
% the polynomial
D4_poly=   1.0e+06 * [  -0.000001003321333
   0.000108002928093
  -0.004647941272734
   0.099959233380745
  -1.074286120871490
   4.615719487403345];

D4_fn = matlabFunction(poly2sym(D4_poly));
subplot(2,2,1);fplot(D4_fn,[19.999825010467916,23.158281544048581])

% using conv
SqD4_poly = conv(D4_poly',D4_poly');

SqD4_fn = matlabFunction(poly2sym(SqD4_poly));
subplot(2,2,2);fplot(SqD4_fn,[19.999825010467916,23.158281544048581])

% using poly2sym
temp = poly2sym(D4_poly);

SqD4_s_fn = matlabFunction(temp ^2);
subplot(2,2,3);fplot(SqD4_s_fn,[19.999825010467916,23.158281544048581])

% sym2poly
SqD4_poly_2 = sym2poly(temp ^2);

SqD4_3_fn = matlabFunction(poly2sym(SqD4_poly_2));
subplot(2,2,4);fplot(SqD4_3_fn,[19.999825010467916,23.158281544048581])

Answer 1

[Matt J]

To avoid the numerical instabilities of high order polynomials, don't work with the coefficients of D4_poly^2. Just evaluate D4_poly at the desired x and square the result:

D4_poly=   1.0e+06 * [  -0.000001003321333
   0.000108002928093
  -0.004647941272734
   0.099959233380745
  -1.074286120871490
   4.615719487403345];

fcn=@(x)polyval(D4_poly,x).^2;

fplot(fcn, [19.999825010467916,23.158281544048581] ); axis tight

[Qiang Li]

Matt, thx for pointing out the stability issue with high order polynomials.