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Least-Squares Polynomial Filters for Ill-Conditioned Linear Systems

Abstract : An important problem which arises in several applications is to find the solution of an ill-conditioned Symmetric Semi-Positive Definite linear system whose right-hand side is perturbed by noise. In this situation, it is desirable for the solution to be accurate in the directions of eigenvectors associated with large eigenvalues, and to have small components in the space associated with smallest eigenvalues. A method is presented to satisfy these requirements, which is based on constructing a polynomial filter using least-squares techniques.
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Submitted on : Wednesday, May 24, 2006 - 9:59:15 AM
Last modification on : Friday, February 4, 2022 - 4:06:53 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:08:12 PM


  • HAL Id : inria-00072447, version 1


Jocelyne Erhel, Frédéric Guyomarc'H, Yousef Saad. Least-Squares Polynomial Filters for Ill-Conditioned Linear Systems. [Research Report] RR-4175, INRIA. 2001. ⟨inria-00072447⟩



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