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mschauer authored Sep 1, 2022
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## Implementation details

The current implementation is based on the [MATLAB version](http://ta.twi.tudelft.nl/nw/users/gijzen/idrs.m) by Van Gijzen and Sonneveld. For background see [^Sonneveld2008], [^VanGijzen2011] and [the IDR(s) webpage](http://ta.twi.tudelft.nl/nw/users/gijzen/IDR.html).
The current implementation is based on the [MATLAB version](http://ta.twi.tudelft.nl/nw/users/gijzen/idrs.m) by
Van Gijzen and Sonneveld. For background see [^Sonneveld2008], [^VanGijzen2011], [the IDR(s) webpage](http://homepage.tudelft.nl/1w5b5/idrs-software.html)
and the IDR chapter in [^Meurant2020].

[^Sonneveld2008]: IDR(s): a family of simple and fast algorithms for solving large nonsymmetric linear systems. P. Sonneveld and M. B. van Gijzen SIAM J. Sci. Comput. Vol. 31, No. 2, pp. 1035--1062, 2008
[^VanGijzen2011]: Algorithm 913: An Elegant IDR(s) Variant that Efficiently Exploits Bi-orthogonality Properties. M. B. van Gijzen and P. Sonneveld ACM Trans. Math. Software,, Vol. 38, No. 1, pp. 5:1-5:19, 2011
[^VanGijzen2011]: Algorithm 913: An Elegant IDR(s) Variant that Efficiently Exploits Bi-orthogonality Properties. M. B. van Gijzen and P. Sonneveld ACM Trans. Math. Software, Vol. 38, No. 1, pp. 5:1-5:19, 2011
[^Meurant2020]: The IDR family. G. Meurant and J. Duintjer Tebbens. In: Krylov Methods for Nonsymmetric Linear Systems. Springer Series in Computational Mathematics, vol 57. Springer, 2020. [doi:10.1007/978-3-030-55251-0_10](https://doi.org/10.1007/978-3-030-55251-0_10)

A deterministic seed is used for generating pseudo-random initial
data for the algorithm; this can be controlled by passing a
different pseudorandom number generator (an [`AbstractRNG`](https://docs.julialang.org/en/v1/stdlib/Random/#Random.AbstractRNG)) via
the `rng` keyword argument.
the `rng` keyword argument.

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