Preconditioned iterative methods for solving linear least squares problems
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 described. First, direct preconditioning of the normal equations by the balanced incomplete factorization (BIF) for symmetri...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/54661 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/54661 |
| Access Level: | acceso abierto |
| Palabra clave: | Preconditioned iterative methods Incomplete decompositions Approximate inverses Linear least squares MATEMATICA APLICADA |
| Sumario: | 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 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. |
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