High dimension matrix algebra

Hi there,

I'm trying to solve a set of linear equations by using Matlab syntax '\'. This properly works for dimensions less than 100000-by-100000. But for higher orders it starts to produce an error regarding the lack of enough memory and for dimensions greater than one million it says maximum variable size is exceeded.

Please help me to see how can I tackle this problem. I have a 10000000-by-10000000 set of equations to solve.

Answer 1

[Jan]

To store a 10000000-by-10000000 matrix you need 800TB Memory - assuming that it is full. As a rule of thumb the double size of free memory is recommended.

Do you see the problem?

[Pouya Jamali]

I see the problem. but how do they tackle such issues in fluid dynamics? It usually happens in systems with small grid cells.

Does it make sense if the coefficient matrix is sparse?

[Jan]

Yes, Pouya, sparsity is the magic word here.

[Pouya Jamali]

But Matlab doesn't even allow me to make a Matrix of zeros of that size!

[Matt J]

That's what the sparse() command is for...so you don't have to allocate all the zeros occurring in your matrix.

Answer 2

[Matt J]

You may have to use pcg() or some other iterative method.

[Pouya Jamali]

I can't workaround your suggestion because Matlab even doesn't allow me to use zeros for pre-allocating this space to the coefficient matrix.

[Matt J]

This properly works for dimensions less than 100000-by-100000.

I'm pretty amazed you were able to get this to work on non-sparse matrices of that size. You must have a tonne of RAM.