Optimizing Multidimensional Regression with Least Squares and Pseudoinverse

[mhill]

i have this problem, given a series of values (x_{i} , y_{j} , z_{k}) =U

could we find a plane 0=Ax+By+Cz+D so the distance from the set of points given in 'U' and the plane with normal vector N=(A,B,C) is a minimum,

or in more general case the distance from the set of points 'U' and the function 0=g(x,y,z) is a minimum , as a certain generalization to the 'least square problem' but in arbitrary dimension

 

[Peeter]

Here's a starting point for you:

http://en.wikipedia.org/wiki/Moore-Penrose_pseudoinverse
http://en.wikipedia.org/wiki/Singular_value_decomposition