Computing the Pseudoinverse of Specific Toeplitz Matrices Using Rank-One Updates

Algorithm 3

function alg41 = alg41(A)

%***************************%

% General Information.    %

%***************************%

% Synopsis:

% alg41 = alg41(A)

% Input:

% A = the initial matrix of interest.

% Output:

% alg41 = mp-inverse by using rank-one updates and the Sherman_Morrison formula.

% This function follows Algorithm 1.

% The correct performance of alg41b requires the presence of yltXl function.

Astar = A’;

m,n = size(A);

G0 = zeros(m,m);

if m > 1

  for i = 1:m-1

  Gkout = G0+A(:,i)*Astar(i,:);

  G0 = Gkout;

  end

  Gm = Gkout+A(:,m)*Astar(m,:);

  else

  Gm = G0;

end

Gkout = Gm;

Y02 = Gkout∖A;

X02 = Y02’;

for l = m+1:n-1

yltout,Xlout = yltXl(Y02,X02,Astar,l,m,n);

Y02 = yltout;

X02 = Xlout;

end

alg41 = X02 - Astar*Y02(:,n)*Y02(:,n)’/(1+Astar(n,:)*Y02(:,n));