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This paper describes a technique for constructing block SOR methods for the solution of the large and sparse indefinite least squares problem which involves minimizing a certain type of indefinite quadratic form. Two block SOR-based algorithms and convergence results are presented. The optimum parameters for the methods are also given. It has been shown both theoretically and numerically that the optimum block SOR methods have a faster convergence than block Jacobi and Gauss-Seidel methods. [ABSTRACT FROM AUTHOR]

Abstract: The hyperbolic modified Gram–Schmidt (HMGS) method is proposed for block downdating the Cholesky factorization. The method might be unsatisfactory due to rounding errors. A modified version based on the MGS process is presented and is shown to be mixed stable. Numerical tests show that the new method has the same numerical properties as the generalized LINPACK-type algorithm, and can work better than the Householder-based algorithm given by Bojanczyk and Steinhardt (1991) . [ABSTRACT FROM AUTHOR]