TY  - GEN 
T1  - Preconditioned iterative methods for solving linear least squares problems
A1  - Bru, Rafael
A1  - Marín, José
A1  - Mas, José
A1  - Tůma, Miroslav
Y1  - 2014
N2  - New preconditioning strategies for solving m × n overdetermined large and sparse linear least squares problems using the CGLS method are described. First, direct preconditioning of the normal equations by the Balanced Incomplete Factorization (BIF) for symmetric and positive definite matrices is studied and a new breakdown-free strategy is proposed. Preconditioning based on the incomplete LU factors of an n × n submatrix of the system matrix is our second approach. A new way to find this submatrix based on a specific weighted transversal problem is proposed. Numerical experiments demonstrate different algebraic and implementational features of the new approaches and put them into the context of current progress in preconditioning of CGLS. It is shown, in particular, that the robustness demonstrated earlier by the BIF preconditioning strategy transfers into the linear least squares solvers and the use of the weighted transversal helps to improve the LU-based approach.
M1  - Preprint project = NCMM
M1  - Preprint year = 2014
M1  - Preprint number = 16
M1  - Preprint ID = NCMM/2014/16
ER  -