an:04201484
Zbl 0727.65034
Vanderbei, Robert J.
Splitting dense columns in sparse linear systems
EN
Linear Algebra Appl. 152, 107-117 (1991).
0024-3795
1991
j
65F30 65F50 65K05
splitting dense columns; sparse matrix; interior-point methods; linear programming; non-symmetric matrices
Let \(A=[S,D]\) where S and D denote respectively the sparse and dense columns of a matrix A. The author gives an efficient and robust method for solving \(AA^ Tx=b.\) The proposed method avoids the rank-deficiency problem that is common to the present algorithms and also makes an effective use of sparse matrix techniques. Applications to interior-point methods for linear programming and non-symmetric matrices are pointed out.
R.P.Tewarson (Stony Brook)