Pseudo-inverse

Pseudo-inverse is specially designed to factorize a matrix for pseudo-inverse to solve the normal equation: A*x = b.
There are two advantages of pseudo-inverse compared to MATLAB pinv:

• PINV requires costly SVD
• PINV does not operated with sparse matrix.
  

The solution x minimize the 2-norm of the residual |Ax - b|. In case of underdetermined system, i.e., rank(A) < length(x), the solution returned by pseudoinverse(A)*b is the least 2-norm among all solutions. Please note that this property does not meet if backslash operator is used: x = Ab.
The method is to use QR factorization on both source and destination space. The factorized result is stored in object that can be used later to multiply with any target space vectors (RHS).

Enhancements:

• Detect SuiteSparseQR package to carry out QR factorization on sparse matrix, not available for Matlab prior 2009B

Requirements:

• MATLAB 7.9 (2009b) 
• Full object oriented supported Matlab version