How can I get good matrix approximations using a sparse matrix?

I have a matrix A (dimension 4000000 x 5) and a sparse matrix B (dimension 4000000 x 2000000). Now I am searching for an approximation of X: A * X = B

Also I need an approximation for Y: A * Y * A' = C (C is a sparse 4000000 x 4000000 matrix)

Answer 1

[Matt J]

 X=A\B;

 Y=A\C/A';

[Steffen]

Error using \

Out of memory. Type HELP MEMORY for your options.

[Matt J]

Ah well. Then alternatively

 Ap=pinv(A);

 X=Ap*B;
 Y=Ap*C*Ap';

[Steffen]

This works but I can't calculate

A * X

afterwards without getting the memory error.