Skyline storage is only for symetric matrices?

[Ronankeating]

hi all,

Is that skyline storage,which is been widely used in FEM problems, is only for symetric matrices?

What if I have non-standardized matrices, that is , which can not be made symettric, has pretty randomly oriented inner products, which can not be put into any computerized manner for storage, so I have to store all of it. What is the general solution for such kind of problems?

Regards,

 

[AlephZero]

Is that skyline storage,which is been widely used in FEM problems, is only for symetric matrices?

There are two meanings of "symmetric" that are relevant to that question.

(1) The pattern of zeros in the matrix is symmetric, i.e. there are many pairs of elements where [itex]a_{i,j} = a_{j,i} = 0[/itex]. (There may be some unpaired zero elements as well, but they are treated the same way as non-zero terms.)

(2) The stronger condition that [itex]a_{i,j} = a^*_{j,i}[/itex] for all values [itex]i[/itex] and [itex]j[/itex]. (Real symmetric matrices are just a special case of complex Hermitian matrices, for most numerical methods).

The basic idea of skyline storage usually refers to (2).

You can use skyline storage for (1) by splitting the matrix in two along the diagonal, and storing the data in two identical shaped "skylines", one vertical and one horizontal. This works well for many purposes when the non-zero data in the matrix is not symmetric.

What if I have non-standardized matrices, that is , which can not be made symettric, has pretty randomly oriented inner products, which can not be put into any computerized manner for storage, so I have to store all of it. What is the general solution for such kind of problems?

The answer depends what you want to do with the sparse matrix. There isn't really a "one size fits all" general solution.