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On the solution of equality constrained quadratic programming problems arising . . .
, 1998
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High Performance Algorithms To Solve Toeplitz And Block Toeplitz Matrices
, 1996
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Projected Krylov Methods for Unsymmetric Augmented Systems
, 2008
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Les textes publiés dans la série des rapports de recherche HEC n’engagent que la responsabilite ́ de leurs auteurs. La publication de ces rapports de recherche bénéficie d’une subvention du Fonds québécois de la recherche sur la nature et les technologies.
Algorithms for rankdeficient and illconditioned Toeplitz leastsquares and QR factorization
"... In this paper we present two algorithms  one to compute the QR factorization of nearly rankdeficient Toeplitz and block Toeplitz matrices and the other to compute the solution of a severely illconditioned Toeplitz leastsquares problem. The first algorithm is based on adapting the generalized Sch ..."
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In this paper we present two algorithms  one to compute the QR factorization of nearly rankdeficient Toeplitz and block Toeplitz matrices and the other to compute the solution of a severely illconditioned Toeplitz leastsquares problem. The first algorithm is based on adapting the generalized Schur algorithm to Cauchylike matrices and has some rankrevealing capability. The other algorithm is based on adapting the augmented systems method to Toeplitz matrices. This algorithm does not suffer from the numerical inaccuracy of most Levinson and Schurbased schemes proposed in the literature thus far because it avoids forming the normal equations either implicitly or explicitly. Some comparisons with more recent Toeplitz leastsquares algorithms are also presented. 1 Introduction In this paper we present two algorithms  one to compute a rankrevealing QR factorization of a Toeplitz matrix and the other to compute the solution to a severely illconditioned Toeplitz leastsquares probl...