## A generalized successive overrelaxation method for least squares problems.(English)Zbl 0907.65043

A new iterative method (called generalized successive overrelaxation) is given for solving large sparse least squares problems and computing the minimum norm solution to underdetermined consistent linear systems. The method is convergent if the matrix has full column rank. The method involves a matrix $$P$$ as a preconditioner and a parameter $$\rho$$ as an accelerator parameter. By suitable choosing of matrix $$P$$ parallel computations are possible.

### MSC:

 65F20 Numerical solutions to overdetermined systems, pseudoinverses 65F35 Numerical computation of matrix norms, conditioning, scaling 65F10 Iterative numerical methods for linear systems 65F50 Computational methods for sparse matrices
Full Text:

### References:

 [1] Å. Björck,Algorithms for linear least squares problems, in Proceedings of the NATO Advanced Study Institute on Computers Algorithms for Solving Linear Algebraic Equations: The State of the Art, E. Spedicato, ed., Springer-Verlag, Berlin, 1991, pp. 57–92. [2] Å. Björck,Numerical Methods for Least Squares Problems, SIAM, Philadelphia, 1996. · Zbl 0847.65023 [3] R. Freund,A note on two block SOR method for sparse least squares problems, Linear Algebra Appl. 88/89 (1987), pp. 211–221. · Zbl 0621.65060 [4] T. L. Markham, M. Neumann and R. J. Plemmons,Convergence of a direct-iterative method for large scale least squares problems, Linear Algebra Appl. 69 (1985), pp. 155–167. · Zbl 0576.65026 [5] R. S. Varga,Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, N. J., 1962. · Zbl 0133.08602 [6] D. M. Young,Linear Solution of Large Linear Systems, Academic Press, New York and London, 1971. · Zbl 0231.65034
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.