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Tlsqr

Solves large, sparse linear least squares problem, as well as unsymmetric linear systems.

Main features

  • Tlsqr solves any of the three problems below or min ||b - Ax||_2 if damp = 0:
     
    Problem Comments
    Ax = b Matrix A should be large, sparse and non-symmetric.
    min ||b - Ax||_2 Large, sparse linear least squares problem.
    min || (b ; 0) - ( A; damp*I ) x ||_2 Damped large, sparse linear least squares problem.

     
  • Tlsqr uses an iterative (conjugate-gradient-like) method. For further information, see the references in the table below:
     
    Authors Title
    1. C. C. Paige and M. A. Saunders (1982a). LSQR: An algorithm for sparse linear equations and sparse least squares, ACM TOMS 8(1), 43-71.
    2. C. C. Paige and M. A. Saunders (1982b). Algorithm 583. LSQR: Sparse linear equations and least squares problems, ACM TOMS 8(2), 195-209.
    3. M. A. Saunders (1995). Solution of sparse rectangular systems using LSQR and CRAIG, BIT 35, 588-604.

     
  • Operations with both dense and sparse Matlab matrices are efficiently implemented.

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