Dr. Johannes Middeke

Research Area

Matrix Normal Forms

Publications

2018

[Middeke]

Denominator Bounds for Systems of Recurrence Equations using ΠΣ-Extensions

J. Middeke, C. Schneider

In: Advances in Computer Algebra. WWCA 2016., C. Schneider, E. Zima (ed.), Springer Proceedings in Mathematics & Statistics 226, pp. 149-173. 2018. Springer, ISSN 2194-1009. arXiv:1705.00280 [cs.SC]. [doi] [pdf]

[bib]

@incollection{RISC5447,
author = {J. Middeke and C. Schneider},
title = {{Denominator Bounds for Systems of Recurrence Equations using ΠΣ-Extensions}},
booktitle = {{ Advances in Computer Algebra. WWCA 2016.}},
language = {english},
series = {Springer Proceedings in Mathematics & Statistics},
volume = {226},
pages = {149--173},
publisher = {Springer},
isbn_issn = {ISSN 2194-1009},
year = {2018},
note = {arXiv:1705.00280 [cs.SC]},
editor = {C. Schneider and E. Zima},
refereed = {yes},
length = {24},
url = {https://www.doi.org/10.1007/978-3-319-73232-9_7}
}

[Middeke]

Towards a Direct Method for Finding Hypergeometric Solutions of Linear First Order Recurrence Systems

Johannes Middeke, Carsten Schneider

ACM Communications 52(3), pp. 185-187. September 2018. 0000. Extended abstract of the poster presentation at 43st International Symposium on Symbolic and Algebraic Computation (ISSAC'18). [doi] [pdf]

[bib]

@article{RISC6452,
author = {Johannes Middeke and Carsten Schneider},
title = {{Towards a Direct Method for Finding Hypergeometric Solutions of Linear First Order Recurrence Systems}},
language = {english},
abstract = {Issue 205. Poster presentation at ISSAC 2018. Extended abstract appeared in ACM Communications, Vol. 52, No. 3, Issue 205, September 2018.},
journal = {ACM Communications},
volume = {52},
number = {3},
pages = {185--187},
isbn_issn = {0000},
year = {2018},
month = {September},
note = {Extended abstract of the poster presentation at 43st International Symposium on Symbolic and Algebraic Computation (ISSAC'18)},
refereed = {yes},
length = {3},
url = {https://doi.org/10.1145/3313880.3313891}
}

2017

[Middeke]

Denominator Bounds and Polynomial Solutions for Systems of q-Recurrences over K(t) for Constant K

Johannes Middeke

In: Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation, Michael Burr (ed.), Proceedings of International Symposium on Symbolic and Algebraic Computation, pp. 325-332. 2017. 978-1-4503-5064-8.

[bib]

@inproceedings{RISC5489,
author = {Johannes Middeke},
title = {{Denominator Bounds and Polynomial Solutions for Systems of q-Recurrences over K(t) for Constant K}},
booktitle = {{Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation}},
language = {english},
abstract = {We consider systems A_ell(t )y(q^ell t ) + . . . + A 0 (t )y(t ) = b (t ) of higher order q-recurrence equations with rational coefficients. We extend a method for finding a bound on the maximal power of t in the denominator of arbitrary rational solutions y(t ) as well as a method for bounding the degree of polynomial solutions from the scalar case to the systems case. The approach is direct and does not rely on uncoupling or reduction to a first order system. Unlike in the scalar case this usually requires an initial transformation of the system.},
pages = {325--332},
isbn_issn = {978-1-4503-5064-8},
year = {2017},
editor = {Michael Burr},
refereed = {yes},
length = {7},
conferencename = {International Symposium on Symbolic and Algebraic Computation}
}

2016

[Middeke]

Denominator Bounds for Higher Order Systems of Linear Recurrence Equations

J. Middeke, C. Schneider

ACM Communications in Computer Algebra 50(4), pp. 185-187. 2016. ISSN 1932-2240. Extended abstract of the poster presentation at ISSAC 2016. [doi] [pdf] [pdf]

[bib]

@article{RISC5317,
author = {J. Middeke and C. Schneider},
title = {{Denominator Bounds for Higher Order Systems of Linear Recurrence Equations}},
language = {english},
journal = {ACM Communications in Computer Algebra},
volume = {50},
number = {4},
pages = {185--187},
isbn_issn = {ISSN 1932-2240},
year = {2016},
note = {Extended abstract of the poster presentation at ISSAC 2016},
refereed = {no},
length = {2},
url = {http://doi.org/10.1145/3055282.3055298}
}

2012

[Middeke]

DEAM 2 Proceedings

C. Doench, J. Middeke, F. Winkler

Technical report no. 00-00 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). 2012. [pdf]

[bib]

@techreport{RISC4560,
author = {C. Doench and J. Middeke and F. Winkler},
title = {{DEAM 2 Proceedings}},
language = {english},
number = {00-00},
year = {2012},
length = {93},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

2011

[Middeke]

A computational view on normal forms of matrices of Ore polynomials

Johannes Middeke

Research Institute for Symbolic Computation (RISC). PhD Thesis. July 2011. RISC Technical Report 11-10. [pdf]

[bib]

@phdthesis{RISC4377,
author = {Johannes Middeke},
title = {{A computational view on normal forms of matrices of Ore polynomials}},
language = {english},
abstract = {This thesis treats normal forms of matrices over rings of Orepolynomials. The whole thesis is divided in three parts: First, Orepolynomials are described and basic facts about them arerecalled. This part also includes integro-differential operators as anextended example. Second, in the main part we present one- andtwo-sided normal forms of matrices. More precisely, we deal with thePopov normal form, Hermite normal form and the Jacobson normal form. In the last part, we explore an applicationof matrix normal forms to a problem in control theory.},
year = {2011},
month = {July},
translation = {0},
school = {Research Institute for Symbolic Computation (RISC)},
length = {102},
type = {RISC Technical Report 11-10}
}

[Middeke]

A toolbox for the analysis of linear systems with delays

Felix Antritter and Johannes Middeke

In: Proceedings of the 50th IEEE Conference on Decision and Control (CDC 2011), , Proceedings of 50th IEEE Conference on Decision and Control (CDC 2011), pp. -. December 2011. Orlando, Florida, USA, IEEE,

[bib]

@inproceedings{RISC4447,
author = {Felix Antritter and Johannes Middeke},
title = {{A toolbox for the analysis of linear systems with delays}},
booktitle = {{Proceedings of the 50th IEEE Conference on Decision and Control (CDC 2011)}},
language = {english},
pages = {--},
address = {Orlando, Florida, USA},
isbn_issn = {?},
year = {2011},
month = {December},
editor = {?},
refereed = {yes},
organization = {IEEE},
length = {0},
conferencename = {50th IEEE Conference on Decision and Control (CDC 2011)}
}

2010

[Middeke]

Converting between the Popov and the Hermite form of matrices of differential operators using an FGLM-like algorithm

Johannes Middeke

Technical report no. 10-16 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). 2010. [pdf]

[bib]

@techreport{RISC4040,
author = {Johannes Middeke},
title = {{ Converting between the Popov and the Hermite form of matrices of differential operators using an FGLM-like algorithm}},
language = {english},
abstract = {We consider matrices over a ring K [∂; σ , θ] of Ore polynomials over a skew field K . Since thePopov and Hermite normal forms are both Gröbner bases (for term over position and position overterm ordering resp.), the classical FGLM-algorithm provides a method of converting one into theother. In this report we investigate the exact formulation of the FGLM algorithm for not necessarily“zero-dimensional” modules and give an illustrating implementation in Maple. In an additionalsection, we will introduce a second notion of Gröbner bases roughly following [Pau07]. We willshow that these vectorial Gröbner bases correspond to row-reduced matrices.},
number = {10-16},
year = {2010},
length = {45},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

[Middeke]

Conversion between Hermite and Popov normal forms using an FGLM-like approach

Johannes Middeke

Albanian Journal of Mathematics 4(4), pp. 181-193. 2010. AulonaPress, 1930-1235. Special Issue, Applications of Computer Algebra 2010, University of Vlora, Albania.

[bib]

@article{RISC4309,
author = {Johannes Middeke},
title = {{Conversion between Hermite and Popov normal forms using an FGLM-like approach}},
language = {english},
abstract = {We are working with matrices over a ring K[D;sigma,theta] of Orepolynomials over a skew field K. Extending a result of Kojima etal. for usual polynomials it is shown that in this setting theHermite and Popov normal forms correspond to Gröbner bases withrespect to certain orders. The FGLM algorithm is adapted to thissetting and used for converting Popov forms into Hermite formsand vice versa. The approach works for arbitrary, ie, notnecessarily square matrices where we establish terminationcriteria to deal with infinitely dimensional factor spaces.},
journal = {Albanian Journal of Mathematics},
volume = {4},
number = {4},
pages = {181--193},
publisher = {AulonaPress},
isbn_issn = {1930-1235},
year = {2010},
note = {Special Issue, Applications of Computer Algebra 2010, University of Vlora, Albania},
refereed = {yes},
length = {13}
}

2009

[Middeke]

Proceedings of DEAM (Workshop for Differential Equations by Algebraic Methods)

Johannes Middeke, Ekaterina Shemyakova, Franz Winkler

Technical report no. 09-08 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). 2009. Proceedings. [pdf]

[bib]

@techreport{RISC3833,
author = {Johannes Middeke and Ekaterina Shemyakova and Franz Winkler},
title = {{Proceedings of DEAM (Workshop for Differential Equations by Algebraic Methods)}},
language = {english},
abstract = {From the 6th of February to the 8th of February 2009, the research project DIFFOP of RISC hosted a workshop about differential equations by algebraic methods (DEAM). The workshop took place in Hagenberg, Austria, in the RISC castle. The main focus was on differential operators and differential polynomials.},
number = {09-08},
year = {2009},
keywords = {DEAM DIFFOP differential equations algebraic methods workshop 2009 proceedings},
sponsor = {The research project �DIFFOP (Symbolic and Algebraic Methods for LPDOs)� is funded by the Austrian Science Fund (FWF) under Nr. P20336-N18},
length = {147},
type = {Proceedings},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

[Middeke]

A skew polynomial approach to integro-differential operators

Georg Regensburger, Markus Rosenkranz, Johannes Middeke

In: Proceedings of ISSAC 2009, Jeremy R. Johnson, Hyungju Park, Erich Kaltofen (ed.), Proceedings of Symbolic and Algebraic Computation, International Symposium, ISSAC 2009, pp. 287-294. 2009. ACM, 978-1-60558-609-0. [url] [pdf]

[bib]

@inproceedings{RISC4025,
author = {Georg Regensburger and Markus Rosenkranz and Johannes Middeke},
title = {{A skew polynomial approach to integro-differential operators}},
booktitle = {{Proceedings of ISSAC 2009}},
language = {english},
abstract = {We construct the algebra of integro-differential operators over anordinary integro-differential algebra directly in terms of normalforms. In the case of polynomial coefficients, we use skewpolynomials for defining the integro-differential Weyl algebra as anatural extension of the classical Weyl algebra in one variable. Its normal forms, algebraic properties and its relation to thelocalization of differential operators are studied. Fixing theintegration constant, we regain the integro-differential operatorswith polynomial coefficients.},
pages = {287--294},
publisher = {ACM},
isbn_issn = {978-1-60558-609-0},
year = {2009},
editor = {Jeremy R. Johnson and Hyungju Park and Erich Kaltofen},
refereed = {yes},
length = {8},
conferencename = {Symbolic and Algebraic Computation, International Symposium, ISSAC 2009},
url = {http://issac2009.kias.re.kr/}
}

2008

[Middeke]

A polynomial-time algorithm for the Jacobson form for matrices of differential operators

Johannes Middeke

Submitted to the RISC Report Series. Technical report no. 08-13 in RISC Report Series, July 2008. [pdf]

[bib]

@techreport{RISC3455,
author = {Johannes Middeke},
title = {{A polynomial-time algorithm for the Jacobson form for matrices of differential operators }},
language = {english},
year = {2008},
month = {July},
howpublished = {Technical report no. 08-13 in RISC Report Series},
length = {17},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}