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Documents authored by Rump, Siegfried M.


Document
Reliable Computation and Complexity on the Reals (Dagstuhl Seminar 17481)

Authors: Norbert T. Müller, Siegfried M. Rump, Klaus Weihrauch, and Martin Ziegler

Published in: Dagstuhl Reports, Volume 7, Issue 11 (2018)


Abstract
Naive computations with real numbers on computers may cause serious errors. In traditional numerical computation these errors are often neglected or, more seriously, not identified. Two approaches attack this problem and investigate its background, Reliable Computing and Computable Analysis. Methods in Reliable Computing are essentially mathematical theorems, the assumptions of which are verified on the computer. This verification is performed using the very efficient floating point arithmetic. If the verification succeeds, the assertions are true and correct error bounds have been computed; if not, a corresponding message is given. Thus the results are always mathematically correct. A specific advantage of Reliable Computing is that imprecise data are accepted; the challenge is to develop mathematical theorems the assumptions of which can be verified effectively in floating-point and to produce narrow bounds for the solution. Computable Analysis extends the traditional theory of computability on countable sets to the real numbers and more general spaces by refining continuity to computability. Numerous even basic and simple problems are not computable since they cannot be solved continuously. In many cases computability can be refined to computational complexity which is the time or space a Turing machine needs to compute a result with given precision. By treating precision as a parameter, this goes far beyond the restrictions of double precision arithmetic used in Reliable computing. For practical purposes, however, the asymptotic results from complexity theory must be refined. Software libraries provide efficient implementations for exact real computations. Both approaches are established theories with numerous important results. However, despite of their obvious close relations these two areas are developing almost independently. For exploring possibilities of closer contact we have invited experts from both areas to this seminar. For improving the mutual understanding some tutorial-like talks have been included in the program. As a result of the seminar it can be stated that interesting joint research is possible.

Cite as

Norbert T. Müller, Siegfried M. Rump, Klaus Weihrauch, and Martin Ziegler. Reliable Computation and Complexity on the Reals (Dagstuhl Seminar 17481). In Dagstuhl Reports, Volume 7, Issue 11, pp. 142-167, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


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@Article{muller_et_al:DagRep.7.11.142,
  author =	{M\"{u}ller, Norbert T. and Rump, Siegfried M. and Weihrauch, Klaus and Ziegler, Martin},
  title =	{{ Reliable Computation and Complexity on the Reals (Dagstuhl Seminar 17481)}},
  pages =	{142--167},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2018},
  volume =	{7},
  number =	{11},
  editor =	{M\"{u}ller, Norbert T. and Rump, Siegfried M. and Weihrauch, Klaus and Ziegler, Martin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.7.11.142},
  URN =		{urn:nbn:de:0030-drops-86826},
  doi =		{10.4230/DagRep.7.11.142},
  annote =	{Keywords: Computable Analysis, Verification Methods, Real Complexity Theory, Reliable Computing}
}
Document
09471 Abstracts Collection – Computer-assisted proofs - tools, methods and applications

Authors: Malcolm B. Brown, Erich Kaltofen, Shin'ichi Oishi, and Siegfried M. Rump

Published in: Dagstuhl Seminar Proceedings, Volume 9471, Computer-assisted proofs - tools, methods and applications (2010)


Abstract
From 15.11. to 20.11.2009, the Dagstuhl Seminar 09471 ``Computer-assisted proofs - tools, methods and applications '' was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.

Cite as

Malcolm B. Brown, Erich Kaltofen, Shin'ichi Oishi, and Siegfried M. Rump. 09471 Abstracts Collection – Computer-assisted proofs - tools, methods and applications. In Computer-assisted proofs - tools, methods and applications. Dagstuhl Seminar Proceedings, Volume 9471, pp. 1-24, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2010)


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@InProceedings{brown_et_al:DagSemProc.09471.1,
  author =	{Brown, Malcolm B. and Kaltofen, Erich and Oishi, Shin'ichi and Rump, Siegfried M.},
  title =	{{09471 Abstracts Collection – Computer-assisted proofs - tools, methods and applications}},
  booktitle =	{Computer-assisted proofs - tools, methods and applications},
  pages =	{1--24},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9471},
  editor =	{B. Malcolm Brown and Erich Kaltofen and Shin'ichi Oishi and Siegfried M. Rump},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09471.1},
  URN =		{urn:nbn:de:0030-drops-25328},
  doi =		{10.4230/DagSemProc.09471.1},
  annote =	{Keywords: Verification methods, computer algebra, computer-assisted proofs}
}
Document
09471 Executive Summary – Computer-assisted proofs - tools, methods and applications

Authors: Malcolm B. Brown, Erich Kaltofen, Shin'ichi Oishi, and Siegfried M. Rump

Published in: Dagstuhl Seminar Proceedings, Volume 9471, Computer-assisted proofs - tools, methods and applications (2010)


Abstract
From November 15-20, 2009, the Dagstuhl seminar on "Computer-assisted proofs - tools, methods and applications" continued a series of previous successful seminars. Participants from 10 different countries presented recent results in verification methods, computer algebra, and other computer-assisted-proof related areas. We had lively talks and discussions, during the regular times for talks, during meals and afterwards. In the following links to abstracts and/or the presentation are given were applicable.

Cite as

Malcolm B. Brown, Erich Kaltofen, Shin'ichi Oishi, and Siegfried M. Rump. 09471 Executive Summary – Computer-assisted proofs - tools, methods and applications. In Computer-assisted proofs - tools, methods and applications. Dagstuhl Seminar Proceedings, Volume 9471, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2010)


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@InProceedings{brown_et_al:DagSemProc.09471.2,
  author =	{Brown, Malcolm B. and Kaltofen, Erich and Oishi, Shin'ichi and Rump, Siegfried M.},
  title =	{{09471 Executive Summary – Computer-assisted proofs - tools, methods and applications}},
  booktitle =	{Computer-assisted proofs - tools, methods and applications},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9471},
  editor =	{B. Malcolm Brown and Erich Kaltofen and Shin'ichi Oishi and Siegfried M. Rump},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09471.2},
  URN =		{urn:nbn:de:0030-drops-25316},
  doi =		{10.4230/DagSemProc.09471.2},
  annote =	{Keywords: Verification methods, computer algebra, computer-assisted proofs}
}
Document
05391 Abstracts Collection – Algebraic and Numerical Algorithms and Computer-assisted Proofs

Authors: Bruno Buchberger, Shin'ichi Oishi, Michael Plum, and Siegfried M. Rump

Published in: Dagstuhl Seminar Proceedings, Volume 5391, Algebraic and Numerical Algorithms and Computer-assisted Proofs (2006)


Abstract
From 25.09.05 to 30.09.05, the Dagstuhl Seminar 05391 ``Algebraic and Numerical Algorithms and Computer-assisted Proofs'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. Links to extended abstracts or full papers are provided, if available.

Cite as

Bruno Buchberger, Shin'ichi Oishi, Michael Plum, and Siegfried M. Rump. 05391 Abstracts Collection – Algebraic and Numerical Algorithms and Computer-assisted Proofs. In Algebraic and Numerical Algorithms and Computer-assisted Proofs. Dagstuhl Seminar Proceedings, Volume 5391, pp. 1-15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2006)


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@InProceedings{buchberger_et_al:DagSemProc.05391.1,
  author =	{Buchberger, Bruno and Oishi, Shin'ichi and Plum, Michael and Rump, Siegfried M.},
  title =	{{05391 Abstracts Collection – Algebraic and Numerical Algorithms and Computer-assisted Proofs}},
  booktitle =	{Algebraic and Numerical Algorithms and Computer-assisted Proofs},
  pages =	{1--15},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{5391},
  editor =	{Bruno Buchberger and Shin'ichi Oishi and Michael Plum and Sigfried M. Rump},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05391.1},
  URN =		{urn:nbn:de:0030-drops-4555},
  doi =		{10.4230/DagSemProc.05391.1},
  annote =	{Keywords: Self-validating methods, computer algebra, computer-assisted proofs, real number algorithms}
}
Document
05391 Executive Summary – Numerical and Algebraic Algorithms and Computer-assisted Proofs

Authors: Bruno Buchberger, Christian Jansson, Shin'ichi Oishi, Michael Plum, and Siegfried M. Rump

Published in: Dagstuhl Seminar Proceedings, Volume 5391, Algebraic and Numerical Algorithms and Computer-assisted Proofs (2006)


Abstract
The common goal of self-validating methods and computer algebra methods is to solve mathematical problems with complete rigor and with the aid of computers. The seminar focused on several aspects of such methods for computer-assisted proofs.

Cite as

Bruno Buchberger, Christian Jansson, Shin'ichi Oishi, Michael Plum, and Siegfried M. Rump. 05391 Executive Summary – Numerical and Algebraic Algorithms and Computer-assisted Proofs. In Algebraic and Numerical Algorithms and Computer-assisted Proofs. Dagstuhl Seminar Proceedings, Volume 5391, pp. 1-5, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2006)


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@InProceedings{buchberger_et_al:DagSemProc.05391.2,
  author =	{Buchberger, Bruno and Jansson, Christian and Oishi, Shin'ichi and Plum, Michael and Rump, Siegfried M.},
  title =	{{05391 Executive Summary – Numerical and Algebraic Algorithms and Computer-assisted Proofs}},
  booktitle =	{Algebraic and Numerical Algorithms and Computer-assisted Proofs},
  pages =	{1--5},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{5391},
  editor =	{Bruno Buchberger and Shin'ichi Oishi and Michael Plum and Sigfried M. Rump},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05391.2},
  URN =		{urn:nbn:de:0030-drops-4549},
  doi =		{10.4230/DagSemProc.05391.2},
  annote =	{Keywords: Self-validating methods, computer algebra, computer-assisted proofs, real number algorithms}
}
Document
Theoretical and Computational Aspects of Matrix Algorithms (Dagstuhl Seminar 03421)

Authors: Nick Higham, Volker Mehrmann, Siegfried M. Rump, and Daniel B. Szyld

Published in: Dagstuhl Seminar Reports. Dagstuhl Seminar Reports, Volume 1 (2021)


Abstract

Cite as

Nick Higham, Volker Mehrmann, Siegfried M. Rump, and Daniel B. Szyld. Theoretical and Computational Aspects of Matrix Algorithms (Dagstuhl Seminar 03421). Dagstuhl Seminar Report 398, pp. 1-5, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2003)


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@TechReport{higham_et_al:DagSemRep.398,
  author =	{Higham, Nick and Mehrmann, Volker and Rump, Siegfried M. and Szyld, Daniel B.},
  title =	{{Theoretical and Computational Aspects of Matrix Algorithms (Dagstuhl Seminar 03421)}},
  pages =	{1--5},
  ISSN =	{1619-0203},
  year =	{2003},
  type = 	{Dagstuhl Seminar Report},
  number =	{398},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemRep.398},
  URN =		{urn:nbn:de:0030-drops-152786},
  doi =		{10.4230/DagSemRep.398},
}
Document
Symbolic-algebraic Methods and Verification Methods - Theory and Applications (Dagstuhl Seminar 99471)

Authors: Götz Alefeld, Jiri Rohn, Siegfried M. Rump, and Tesuro Yamamoto

Published in: Dagstuhl Seminar Reports. Dagstuhl Seminar Reports, Volume 1 (2021)


Abstract

Cite as

Götz Alefeld, Jiri Rohn, Siegfried M. Rump, and Tesuro Yamamoto. Symbolic-algebraic Methods and Verification Methods - Theory and Applications (Dagstuhl Seminar 99471). Dagstuhl Seminar Report 260, pp. 1-34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2000)


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@TechReport{alefeld_et_al:DagSemRep.260,
  author =	{Alefeld, G\"{o}tz and Rohn, Jiri and Rump, Siegfried M. and Yamamoto, Tesuro},
  title =	{{Symbolic-algebraic Methods and Verification Methods - Theory and Applications (Dagstuhl Seminar 99471)}},
  pages =	{1--34},
  ISSN =	{1619-0203},
  year =	{2000},
  type = 	{Dagstuhl Seminar Report},
  number =	{260},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemRep.260},
  URN =		{urn:nbn:de:0030-drops-151457},
  doi =		{10.4230/DagSemRep.260},
}
Document
Symbolic, Algebraic and Validated Numerical Computation (Dagstuhl Seminar 9232)

Authors: James H. Davenport, Fritz Krückeberg, Ramon E. More, and Siegfried M. Rump

Published in: Dagstuhl Seminar Reports. Dagstuhl Seminar Reports, Volume 1 (2021)


Abstract

Cite as

James H. Davenport, Fritz Krückeberg, Ramon E. More, and Siegfried M. Rump. Symbolic, Algebraic and Validated Numerical Computation (Dagstuhl Seminar 9232). Dagstuhl Seminar Report 43, pp. 1-20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (1992)


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@TechReport{davenport_et_al:DagSemRep.43,
  author =	{Davenport, James H. and Kr\"{u}ckeberg, Fritz and More, Ramon E. and Rump, Siegfried M.},
  title =	{{Symbolic, Algebraic and Validated Numerical Computation (Dagstuhl Seminar 9232)}},
  pages =	{1--20},
  ISSN =	{1619-0203},
  year =	{1992},
  type = 	{Dagstuhl Seminar Report},
  number =	{43},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemRep.43},
  URN =		{urn:nbn:de:0030-drops-149318},
  doi =		{10.4230/DagSemRep.43},
}
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