1974•Journal of the ACMOpen access

Linear Least Squares by Elimination and MGS

Robert J. Plemmons

Abstract

An algorithm combining Gaussian elimination with the modified Gram-Schmidt (MGS) procedure is given for solving the linear least squares problem. The method is based on the operational efficiency of Gaussian elimination for LU decompositions and the numerical stability of MGS for unitary decompositions and is designed for slightly overdetermined linear systems.

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Key concepts: Overdetermined system, Gaussian elimination, Mathematics, Least-squares function approximation, Applied mathematics, Gaussian, Linear least squares, Linear system