## Dealing with dense rows in the solution of sparse linear least squares problems |

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Advanced Computing Research algorithm SLS backslash operator badly conditioned Cholesky factorization Chunguang Sun Computing Research Institute condition number containing relatively dense Cornell Theory Center denoted Fadil Santosa full column rank function SLS J. A. George least squares problems linear least squares m-by-r dense matrix MATLAB 4.2c n x n upper triangular number of nonzeros numerical experiments optimal partition optimal value orthogonal matrix output argument performance results permutation matrix popt problems containing relatively relatively dense rows row.len running time curve satisfactory partition satisfies the tolerance scfxm2 scrs8 shown in Fig SLS in Fig Solution of Sparse solution updating algorithm solution xo Solve the sparse solving sparse linear sparse linear least sparse LS problem sparse matrix sparse QR factorization sparse rows sparsity threshold parameter SPLS spls(A squares problems containing straightforward approach submatrix test problems triangular factor updating the solution upper triangular matrix vector Wei Yuan Written by Chunguang X B an m-by-r Yuying