In this paper we consider a geometric viewpoint to analyze the behaviour of the Conjugate Gradient (CG) method, for the solution of a symmetric linear system, when at current step a pivot breakdown possibly occurs (degenerate case). As well known this can occur when the system matrix is indefinite or singular. In the latter case the CG gets stuck, since the steplength along the current search direction cannot be computed. We show here that a simple geometric interpretation can be provided for the degenerate case, as long as some basics on projective geometry in the Euclidean space arc considered.
|Data di pubblicazione:||2016|
|Titolo:||Polarity for Quadratic Hypersurfaces and Conjugate Gradient Method: Relation between Degenerate and Nondegenerate Cases|
|Titolo del libro:||Numerical Computations:Theory and Algorithms, The 2nd International Conference and Summer School (NUMTA 2016)|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1063/1.4965395|
|Appare nelle tipologie:||4.1 Articolo in Atti di convegno|