Excerpt More than 25 years have passed since the first edition of this book was published in
1996. Least squares and least-norm problems have become more significant with every …

We describe the design and implementation of a parallel QR decomposition algorithm for a
large sparse matrix A. The algorithm is based on the multifrontal approach and makes use of …

For sparse QR factorization, nding a good column ordering of the matrix to be factorized, is
essential. Both the amount of ll in the resulting factors, and the number of oating-point …

In the recently presented sparse matrix extension of MATLAB, there is no routine for sparse
QR factorization. Sparse linear least-squares problems are instead solved by the …

The rank-revealing QR-factorization (RRQR factorization) is a special QR-factorization that is
guaranteed to reveal the numerical rank of the matrix under consideration. This makes the …

Incremental condition estimation provides an estimate for the smallest singular value of a
triangular matrix. In particular, it gives a running estimate of the smallest singular value of a …

We discuss a parallel shared memory implementation of multifrontal QR factorization. To
achieve high performance for general large and sparse matrices, a combination of tree and …

We describe an algorithm to compute an approximate rank revealing sparse QR
factorization. We use a two phase algorithm to provide especially high accuracy in the …

This thesis addresses topics in sparse least squares computation. A stable method for
solving the least squares problem, minkAx; bk2 is based on the QR factorization. Here we …

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 …