When simulating a mechanism from science or engineering, or an industrial process, one is
frequently required to construct a mathematical model, and then resolve this model …

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 …

Many papers have discussed preconditioned block iterative methods for solving full rank
least-squares problems. However very few papers studied iterative methods for solving rank …

This paper describes a technique for constructing robust preconditioners for the CGLS
method applied to the solution of large and sparse least squares problems. The algorithm …

We propose an alternative iterative method to solve rank deficient problems arising in many
real applications such as the finite element approximation to the Stokes equation and …

The celebrated minimum residual method (MINRES), proposed in the seminal paper of
Paige and Saunders, has seen great success and wide-spread use in solving linear least …

New preconditioning strategies for solving m*n overdetermined large and sparse linear least
squares problems using the conjugate gradient for least squares (CGLS) method are …

We study the solution of the linear least-squares problem \min_x‖b-Ax‖^2_2 where the
matrix A∈\BbbR^m*n (m≥n) has rank n and is large and sparse. We assume that A is …

As an application of the symmetric-triangular (ST) decomposition given by Golub and Yuan
(2001) and Strang (2003), three block ST preconditioners are discussed here for saddle …

We present, implement and test several incomplete QR factorization methods based on
Givens rotations for sparse square and rectangular matrices. For square systems, the …