Symmetric matrix is not symmetric

问题

I have recently written code for finite element method. Since my algorithm is generating a symmetric matrix, after gathering data for each element the resulting matrix should be symmetric.

However, after I run loop over element, the resulting global matrix is not symmetric. The basic code structure is like this:

A=zeros(dof,dof)

for (each element)
    loc_A = v'*(diagonal matrix)*v
         % (v is 1xN row vector)
         % loc_A is symmetric matrix

    A(K,K) = A(K,K)+loc_A
                 % (K is Nx1 column vector)
end

Since I add symmetric matrices, the resulting matrix should also be symmetric.

However, the resulting matrix is not symmetric (I checked it with issymmetric(A)). I think this is because of round-off error. If I add A=(A+A')/2, resulting matrix is symmetric (of course...). However I don't want to do such thing. Is there any other remedy which makes A symmetric naturally without any post-processing?

回答1:

This is due to round-off error (unless you have an obvious bug in your code). This issue is normally solved by A = (A+A')/2 (this is not an expensive operation) or you can tell the solver that your global matrix is symmetric (some solvers (i.e. MUMPS) have such an option.)

来源：https://stackoverflow.com/questions/37648152/symmetric-matrix-is-not-symmetric