Solve large linear equation on GPU

Hi, I need to solve a large linear equation A*X=B on GPU, however A is large symetric matrix A(n, n) with n > 100.000 (may be bad scaled), and it result in an out of memory. Is there any way to split this matrix into smaller sub matrix and solve this problem in iterative way on gpu?

Thx

Answer 1

[Joss Knight]

If you look online, or perhaps read a book like Golub and van Loan you can find block-based parallel or sequential formulations of the basic steps of the solve (in your case, Cholesky factorisation followed by triangular solve). For instance, if you have:

[A11 A21'] = [G11 0  ] * [G11 0  ]'
[A21 A22 ]   [G21 G22]   [G21 G22]

then

A11 = G11*G11'
A21 = G21*G11'
A22 = G21*G21' + G22*G22'

which gives the following procedure:

G11 = chol(A11);
G21 = A21/(G11');
G22 = chol(A22 - G21*G21');

Then you need to do a similar breakdown of the blockwise triangular solve.

You might also try distributed arrays which are deliberately designed for matrices that don't fit in the memory of a single MATLAB client.