Homogeneous system - is there a function that accepts initial estimates?

Hi All! I've a 4x4 matrix A (with 6400-iterations) comprised via data from practical measurements which presents the typical Ax = 0... I wish to find the non-trivial x. A singular value decomposition method of determining a solution has been tried and returns the 'real' solution over a very small band. I have functions that would, with inputted estimates, return ball-park figures for x initially. Can anyone please guide me toward a function that will realise solutions that are nearest a given estimate rather than the first-after-trivial? V. Much Obliged :) Dave.

[tlawren]

So, you know A, and you want x, such that Ax = 0? If this is the case, then what you seek is a vector in the null space of A. If you've got the SVD on hand, then you've got an orthonormal basis for the null space of A inside V. Specifically, if S is a square matrix, then the columns of V associate with diag(S) = 0 form you basis.