Floating Point Accuracy Problem or Human Error?

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William Wooley 2016-9-8

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https://ww2.mathworks.cn/matlabcentral/answers/302409-floating-point-accuracy-problem-or-human-error

评论： William Wooley 2016-9-8

I am trying to check my analytic solutions to a (somewhat ugly) system of equations by using sym/solve.

To preview, my problem is this: It seems that my analytic solutions match up with those returned by solve. The difference between the two solutions is on the order of 1e-16 at most. However, when I then multiply each solution by a vector one of the key coefficients is slightly greater than one in one case and less than one in the other. My (broader) conclusions hinge on this fact.

Here's some pseudo-code of what I'm doing:

syms x y real
z = sym('z',3);
% 'Solve' Solution
to_solve = a * z == b * z + c * (x - d * y) ....;
[zs1,zs2,zs3,zs4] = solve(to_solve,z);
zs = [zs1,zs2,zs3,zs4]';
vpa(zs,4);
  ans = 
   0.05146*y + 7.078*x
   0.1465*y + 0.3384*x
   0.06446*y - 1.776*x
   1.416*x - 0.04118*y 
  % Analytic Solution 
  zas = p * x + q * y;
  vpa(zas,4);
   ans = 
   0.05146*y + 7.078*x
   0.1465*y + 0.3384*x
   0.06446*y - 1.776*x
   1.416*x - 0.04118*y
% Compare - Solutions are very close
disp(vpa(zas - zs,5));
% Test Outcome - Solve for x as ftn of y
to_solve2_s = x == r' * zs;
xs = solve(to_solve2_s,x);
to_solve2_as = x == r' * zas;
xas = solve(to_solve2_as,x);