function x_turv = turv(U,R,V,p,b)%  turv --> Solves a least squares problem using the URV decomposition.%%  <Synopsis>%    x_turv = turv(U,R,V,p,b)%%  <Description>%    Solves the near-rank deficient least squares problem%%           min_x || b-A*x ||_2%%    using the URV decomposition. Here, A = U*R*V' is the URV%    decomposition of A, p is the numerical rank of A, and the%    TURV solution is defined by%%           x_turv = V(:,1:p)*inv(R(1:p,1:p))*U(:,1:p)'*b.%%  <See Also>%    tulv  --> Solves a least squares problem using the ULV decomposition.%    trrqr --> Solves a least squares problem using the RRQR decomposition.%  <Revision>%    Ricardo D. Fierro, California State University San Marcos%    Per Christian Hansen, IMM, Technical University of Denmark%    Peter S.K. Hansen, IMM, Technical University of Denmark%%    Last revised: June 22, 1999%-----------------------------------------------------------------------% Transform right hand side.beta = U(:,1:p)'*b;% Back-substitution.y = R(1:p,1:p)\beta;% Compute TURV solution.x_turv = V(:,1:p)*y;%-----------------------------------------------------------------------% End of function turv%-----------------------------------------------------------------------