pinit.m

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function [T,x_0] = pinit(W,A,b) 
%PINIT Utility init.-procedure for "preconditioned" iterative methods. 
% 
% T = pinit(W,A) 
% [T,x_0] = pinit(W,A,b) 
% 
% Initialization for `preconditioning' of general-form problems. 
% Here, W holds a basis for the null space of L. 
% 
% Determines the matrix T needed in the iterative routines for 
% treating regularization problems in general form. 
% 
% If b is also specified then x_0, the component of the solution in 
% the null space of L, is also computed. 
 
% Reference: P. C. Hansen, "Rank-Deficient and Discrete Ill-Posed Problems. 
% Numerical Aspects of Linear Inversion", SIAM, Philadelphia, 1997. 
 
% Per Christian Hansen, IMM, 07/29/97. 
  
% Initialization. 
[n,nu] = size(W); 
 
% Special treatment of square L. 
if (nu==0), T = []; x_0 = zeros(n,1); return, end 
 
% Compute T. 
S = pinv(A*W); 
T = S*A; 
 
% If required, also compute x_0. 
if (nargin==3), x_0 = W*(S*b); end