Large Scale Weighted Least Squares

Hello,

I would like to use Intel MKL to solve a Large Scale Weighted Least Squares problem.

The Matrices are sparse yet their elements number might be huge.

This is a result of working on images and hence the matrices are the size of (M x N)^2.

My questions are:

1. Which solvers should I use for that?

2. Is there a solver that instead of creating the matrix I can hand it a pointer to function which can calculate each (i, j) element of the matrix and hence eliminate the memory constrain?

3. Can MKL handle sparse matrices of (36e6) ^ 2 elements? How much time should I expect it to take solving: Ax = b where A is 36e6 by 36e6 ?

Thank You.