Numerical Stability of Descent Methods for Solving Linear Equations

@inproceedings{JoA2005NumericalSO,
  title={Numerical Stability of Descent Methods for Solving Linear Equations},
  author={M. JoA.},
  year={2005}
}
  • M. JoA.
  • Published 2005
In this paper we perform a round-off error analysis of descent methods for solving a linear system Ax=b, where A is supposed to be symmetric and positive definite. This leads to a general result on the attainable accuracy of the computed sequence {xi} when the method is performed in floating point arithmetic. The general theory is applied to the Gauss-Southwell method and the gradient method. Both methods appear to be well-behaved which means that these methods compute an approximation xi to… CONTINUE READING