IDR(s): A Family of Simple and Fast Algorithms for Solving Large Nonsymmetric Systems of Linear Equations

@article{Sonneveld2008IDRsAF,
  title={IDR(s): A Family of Simple and Fast Algorithms for Solving Large Nonsymmetric Systems of Linear Equations},
  author={Peter Sonneveld and Martin B. van Gijzen},
  journal={SIAM J. Sci. Comput.},
  year={2008},
  volume={31},
  pages={1035-1062}
}
We present IDR($s$), a new family of efficient, short-recurrence methods for large nonsymmetric systems of linear equations. The new methods are based on the induced dimension reduction (IDR) method proposed by Sonneveld in 1980. IDR($s$) generates residuals that are forced to be in a sequence of nested subspaces. Although IDR($s$) behaves like an iterative method, in exact arithmetic it computes the true solution using at most $N + N/s$ matrix-vector products, with $N$ the problem size and $s… 

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