The direct method of solution of the sparse least squares problem with upper and lower constraints. (Russian) Zbl 0669.65030

Björck, A.

Vychisl. Protsessy Sist. 6, 61-75 (1988).

The author deals with the linear least squares problem under lower and upper constraints on the variables for large sparse matrices. It is shown that the new method of seminormal equations with one correction step assures exact results. An update of the QR factorization of the matrix in the case of column ordering and adding one column at one iteration is a pivotal part of the algorithm. Numerical results confirming the effectiveness of the method for sparse problems are presented.

Reviewer: S.Grzegórski

MSC:

65F20	Numerical solutions to overdetermined systems, pseudoinverses
65K05	Numerical mathematical programming methods
65F50	Computational methods for sparse matrices
65F05	Direct numerical methods for linear systems and matrix inversion
90C20	Quadratic programming

Keywords:

linear least squares problem; lower and upper constraints; large sparse matrices; method of seminormal equations; QR factorization