### Abstract

This paper studies the solution of the linear least squares problem for a large and sparse m by n matrix A with m ≥ n by QR factorization of A and transformation of the right-hand side vector 6 to Q^{T}b. A multifrontal-based method for computing Q^{T}b using Householder factorization is presented. A theoretical operation count for the K by K unbordered grid model problem and problems defined on graphs with √n-separators shows that the proposed method requires O(N_{R}) storage and multiplications to compute Q^{T}b, where N_{R} = O(n log n) is the number of nonzeros of the upper triangular factor R of A. In order to introduce BLAS-2 operations, Schreiber and Van Loan's storage-efficient WY representation [SIAM J. Sci. Stat. Comput., 10 (1989), pp. 53-57] is applied for the orthogonal factor Q_{i} of each frontal matrix F_{i}. If this technique is used, the bound on storage increases to O(n(log n)^{2}). Some numerical results for the grid model problems as well as Harwell-Boeing problems are provided.

Original language | English (US) |
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Pages (from-to) | 658-679 |

Number of pages | 22 |

Journal | SIAM Journal on Matrix Analysis and Applications |

Volume | 17 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jul 1996 |

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### All Science Journal Classification (ASJC) codes

- Analysis