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