Dear collegs,

Let us have a linear system:

Ax=b, (1)

A is a matrix of (N,N) shape, b, x are vectors of N shape. We decrease number of equations to form a underdetermined system:

A'x=b', (2)

A' is a matrix of (M,N) shape, b' is a vector of M shape, M < N.

Can we find any formula for a difference between normal pseudo-solution of the system (2) and exact solution of the system (1)?

Can we find how many equations must we use to estimate exact solution by normal pseudo-solution with the known precision?

Can we determine a convergence rate of the normal pseudo-solution to the exact one in dependence of matrix A parameters (condition number, singular values, etc.)?