Problem: Given 
find 
to minimize 
.
If m > n, in which case we have more equations than the
number of unknowns, there is generally no 
satisfying 
exactly. This is an over-constrained system. There are three
different algorithms for computing the least square minimum. We
list the three methods and compare them in terms of
operations count and the accuracy.
Cheap 
Less Accurate
Expensive 
More reliable
The first algorithm in the fastest and the least accurate
among the three. On the other hand SVD is the slowest and
most accurate, especially when 
is not fully
ranked (i.e. its rank is less than n).
For the first two algorithms, we assume that 
is fully ranked.