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Pseudoinverse preconditioners and iterative methods for large dense linear least-squares problems
Oskar Cahueñas, Luis M. Hernández-Ramos, Marcos Raydan

We address the issue of approximating the pseudoinverse of the coefficient matrix  for dynamically building preconditioning strategies for the numerical solution of large dense linear least-squares problems. The new preconditioning strategies are embedded into simple and well-known iterative  schemes that avoid the use of the, usually ill-conditioned,  normal equations. We analyze a scheme to approximate the pseudoinverse, based on Schulz iterative method, and also different iterative schemes, based on extensions of Richardson's method, and the conjugate gradient method,  that are suitable for preconditioning strategies. We present  preliminary numerical results to illustrate the advantages of the proposed schemes.

Keywords: Schulz method, pseudoinverse, linear least-squares problems, preconditioned Richardson's method, conjugate gradient method

Cite this paper:
Cahueñas O., Hernández-Ramos L.M., Raydan M., Pseudoinverse preconditioners and iterative methods
for large dense linear least-squares problems.
Bull. Comput. Appl. Math. (Bull CompAMa),
Vol. 1, No. 1, Jan-Jun, pp.25-47, 2013