# Periodic Schur decomposition

**URL:** <https://discourse.julialang.org/t/periodic-schur-decomposition/30682>\
**Category:** General Usage\
**Tags:** question\
**Created:** [November 4, 2019, 8:08am UTC](https://discourse.julialang.org/t/periodic-schur-decomposition/30682 "2019-11-04T08:08:19Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![rveltz](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rveltz/32/2707_2.png) [@rveltz](https://discourse.julialang.org/u/rveltz)\
**Post date:** [November 4, 2019, 8:08am UTC](https://discourse.julialang.org/t/periodic-schur-decomposition/30682/1 "2019-11-04T08:08:19Z")

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Hi,

I am wondering if anybody has implemented, and is willing to share, **a periodic Schur decomposition**. The first paper mentioning it is

D. Kressner, **An efficient and reliable implementation of the periodic qz algorithm** IFAC Proceedings Volumes, vol. 34, no. 12, pp. 183–188, 2001.

There seems to be a Fortran code of this algorithm if one asks D. Kressner.

Thank you,

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**Author:** ![Ralph\_Smith](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ralph_smith/32/10344_2.png) [@Ralph\_Smith](https://discourse.julialang.org/u/Ralph_Smith)\
**Post date:** [November 5, 2019, 2:03pm UTC](https://discourse.julialang.org/t/periodic-schur-decomposition/30682/2 "2019-11-05T14:03:01Z")

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IIRC there are routines for this in [SLICOT](https://github.com/KTH-AC/slicot) (a FORTRAN library, under GPL).

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**Author:** ![rveltz](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rveltz/32/2707_2.png) [@rveltz](https://discourse.julialang.org/u/rveltz)\
**Post date:** [November 21, 2019, 1:21pm UTC](https://discourse.julialang.org/t/periodic-schur-decomposition/30682/3 "2019-11-21T13:21:41Z")

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Is it based on the code by Kressner?

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**Author:** ![Ralph\_Smith](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ralph_smith/32/10344_2.png) [@Ralph\_Smith](https://discourse.julialang.org/u/Ralph_Smith)\
**Post date:** [November 21, 2019, 2:31pm UTC](https://discourse.julialang.org/t/periodic-schur-decomposition/30682/4 "2019-11-21T14:31:03Z")

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I think Kressner did contribute to the SLICOT project, but I avoid looking at GPL sources so I’ll let someone else check these particular routines.