How to suppress errors in matrix algebra involving very large matrices ?

Question

Aditya Nanda 2016-12-13

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/316738-how-to-suppress-errors-in-matrix-algebra-involving-very-large-matrices

回答： Aditya Nanda 2017-5-24

I have two very large matrices, A and B which constitute an equation

A* x + B* y =0

I am interested in solving for x (denoted x_star) so

x_star = pinv(A) * (- B*y);

Then, I back- substitute x_star to check the accuracy

A* x_star + B* y

But this value is not zero. Its usually a large number. How do I ensure this is zero? The matrices A and B are given as

y= [1,0]';

A(1,1) = 4.15325070802278e+22 - .07633591784246e+18i ;

A(1,2) = 9.04710238303399e+20- 8.73556649303388e+16i ;

A(2,1) = -9.04710238303399e+20+ .73556649303387e+16i;

A(2,2) = -1.9707469469826e+19 + 1.87151868951167e+15i ;

B(1,1) = 2.57576471264519e+18

B(1,2) = -1.18245242413448e+20 ;

B(2,1) = -5.610835634053e+16 ;

B(2,2 ) = 2.57575785721108e+18;

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Matt J 2016-12-13

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/316738-how-to-suppress-errors-in-matrix-algebra-involving-very-large-matrices#answer_247053

编辑：Matt J 2016-12-13

在 MATLAB Online 中打开

You can't make it zero. To hope for that is to be in denial of the realities of floating point arithmetic. But as for your specific data, the substitution result looks pretty reasonable,

    >> A*x_star+B*y
    ans =
       1.0e+07 *
       0.0001 + 4.5513i
      -0.0000 - 0.0991i

Looks pretty small to me - certainly when compared to the magnitude of the elements of A and B which are O(1e20).

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

Answer 2

Aditya Nanda 2017-5-24

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/316738-how-to-suppress-errors-in-matrix-algebra-involving-very-large-matrices#answer_268245

Just for the sake of documenting, I actually found a way to make this work. Matlab has vpa (variable precision arithmetic), using which it is possible to minimize the error to exactly zero (well, of the order of 1e-100 or even less).

Of course, theres no way to do this using double arithmetic.