A Modified Implementation of MINRES to Monitor Residual Subvector Norms for Block Systems (bibtex)
by Roland Herzog, Kirk M. Soodhalter
Abstract:
Saddle-point systems, i.e., structured linear systems with symmetric matrices are considered. A modified implementation of (preconditioned) MINRES is derived which allows to monitor the norms of the subvectors individually. Compared to the implementation from the textbook of [Elman, Sylvester and Wathen, Oxford University Press, 2014], our method requires one extra vector of storage and no additional applications of the preconditioner. Numerical experiments are included.
Reference:
A Modified Implementation of MINRES to Monitor Residual Subvector Norms for Block Systems (Roland Herzog, Kirk M. Soodhalter), In SIAM J. Sci. Comput., volume 39, 2017. (Matlab code)
Bibtex Entry:
@ARTICLE{HS.2016,
AUTHOR = {Herzog, Roland and Soodhalter, Kirk M.},
     TITLE = {A {M}odified {I}mplementation of {MINRES} to {M}onitor
              {R}esidual {S}ubvector {N}orms for {B}lock {S}ystems},
   JOURNAL = {SIAM J. Sci. Comput.},
  FJOURNAL = {SIAM Journal on Scientific Computing},
    VOLUME = {39},
      YEAR = {2017},
    NUMBER = {6},
     PAGES = {A2645--A2663},
      ISSN = {1064-8275},
   MRCLASS = {65F10 (15B57 65F08 65M22 65N22)},
  MRNUMBER = {3725283},
       URL = {https://doi.org/10.1137/16M1093021},
keywords = {paper},
abstract = {Saddle-point systems, i.e., structured linear systems with symmetric matrices are considered. A modified implementation of (preconditioned) MINRES is derived which allows to monitor the norms of the subvectors individually. Compared to the implementation from the textbook of [Elman, Sylvester and Wathen, Oxford University Press, 2014], our method requires one extra vector of storage and no additional applications of the preconditioner. Numerical experiments are included. },
	comment = {<a href="https://zenodo.org/record/47393?ln=en#.VwZVyT_Nqyo">Matlab code</a>}
}
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