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SUMMARYA sequence of least-squares problems of the form miny G 1=2 (A T y − h) 2 , where G is an n × n positivedeÿnite diagonal weight matrix, and A an m × n (m6n) sparse matrix with some dense columns; has many applications in linear programming, electrical networks, elliptic boundary value problems, and structural analysis. We suggest low-rank correction preconditioners for such problems, and a mixed solver (a combination of a direct solver and an iterative solver). The numerical results show that our technique for selecting the low-rank correction matrix is very e ective.

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