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Documents authored by Bini, Dario A.

Document
DOI: 10.4230/DagSemProc.07461.1
07461 Abstracts Collection – Numerical Methods for Structured Markov Chains

Authors: Dario A. Bini, Beatrice Meini, Vaidyanathan Ramaswami, Marie-Ange Remiche, and Peter Taylor

Published in: Dagstuhl Seminar Proceedings, Volume 7461, Numerical Methods for Structured Markov Chains (2008)

Abstract
From 11.11. to 14.11.07, the Dagstuhl Seminar 07461 ``Numerical Methods for Structured Markov Chains'' 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. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
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Dario A. Bini, Beatrice Meini, Vaidyanathan Ramaswami, Marie-Ange Remiche, and Peter Taylor. 07461 Abstracts Collection – Numerical Methods for Structured Markov Chains. In Numerical Methods for Structured Markov Chains. Dagstuhl Seminar Proceedings, Volume 7461, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{bini_et_al:DagSemProc.07461.1,
  author =	{Bini, Dario A. and Meini, Beatrice and Ramaswami, Vaidyanathan and Remiche, Marie-Ange and Taylor, Peter},
  title =	{{07461 Abstracts Collection – Numerical Methods for Structured Markov Chains}},
  booktitle =	{Numerical Methods for Structured Markov Chains},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7461},
  editor =	{Dario Bini and Beatrice Meini and Vaidyanathan Ramaswami and Marie-Ange Remiche and Peter Taylor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.07461.1},
  URN =		{urn:nbn:de:0030-drops-14046},
  doi =		{10.4230/DagSemProc.07461.1},
  annote =	{Keywords: Matrix analytic methods, markov processes, queuing theory, numerical methods, structured matrices, telecommunication modeling, performance evaluation}
}
Document
DOI: 10.4230/DagSemProc.07461.2
07461 Executive Summary – Numerical Methods for Structured Markov Chains

Authors: Dario A. Bini, Beatrice Meini, Vaidyanathan Ramaswami, Marie-Ange Remiche, and Peter Taylor

Published in: Dagstuhl Seminar Proceedings, Volume 7461, Numerical Methods for Structured Markov Chains (2008)

Abstract
This Dagstuhl seminar has brought together leaders and young researchers in the fields of analysis of numerical algorithms, applied stochastic modeling and statistical inference, with the result of stimulating exchange of methodologies and experiences and generating synergetic collaborations. This has favored a better communication between these worlds where problems from the applications feed the theoretical research and where advanced numerical tools can be utilized in applications with reciprocal advantages.
Cite as

Dario A. Bini, Beatrice Meini, Vaidyanathan Ramaswami, Marie-Ange Remiche, and Peter Taylor. 07461 Executive Summary – Numerical Methods for Structured Markov Chains. In Numerical Methods for Structured Markov Chains. Dagstuhl Seminar Proceedings, Volume 7461, pp. 1-2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{bini_et_al:DagSemProc.07461.2,
  author =	{Bini, Dario A. and Meini, Beatrice and Ramaswami, Vaidyanathan and Remiche, Marie-Ange and Taylor, Peter},
  title =	{{07461 Executive Summary – Numerical Methods for Structured Markov Chains}},
  booktitle =	{Numerical Methods for Structured Markov Chains},
  pages =	{1--2},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7461},
  editor =	{Dario Bini and Beatrice Meini and Vaidyanathan Ramaswami and Marie-Ange Remiche and Peter Taylor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.07461.2},
  URN =		{urn:nbn:de:0030-drops-14006},
  doi =		{10.4230/DagSemProc.07461.2},
  annote =	{Keywords: Matrix analytic methods, Markov processes, queuing theory, numerical methods, structured matrices, telecommunication modeling, performance evaluation.}
}
Document
DOI: 10.4230/DagSemProc.07461.7
From Algebraic Riccati equations to unilateral quadratic matrix equations: old and new algorithms

Authors: Dario A. Bini, Beatrice Meini, and Federico Poloni

Published in: Dagstuhl Seminar Proceedings, Volume 7461, Numerical Methods for Structured Markov Chains (2008)

Abstract
The problem of reducing an algebraic Riccati equation $XCX-AX-XD+B=0$ to a unilateral quadratic matrix equation (UQME) of the kind $PX^2+QX+R$ is analyzed. New reductions are introduced which enable one to prove some theoretical and computational properties. In particular we show that the structure preserving doubling algorithm of B.D.O. Anderson [Internat. J. Control, 1978] is nothing else but the cyclic reduction algorithm applied to a suitable UQME. A new algorithm obtained by complementing our reductions with the shrink-and-shift tech- nique of Ramaswami is presented. Finally, faster algorithms which require some non-singularity conditions, are designed. The non-singularity re- striction is relaxed by introducing a suitable similarity transformation of the Hamiltonian.
Cite as

Dario A. Bini, Beatrice Meini, and Federico Poloni. From Algebraic Riccati equations to unilateral quadratic matrix equations: old and new algorithms. In Numerical Methods for Structured Markov Chains. Dagstuhl Seminar Proceedings, Volume 7461, pp. 1-28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{bini_et_al:DagSemProc.07461.7,
  author =	{Bini, Dario A. and Meini, Beatrice and Poloni, Federico},
  title =	{{From Algebraic Riccati equations to unilateral quadratic matrix equations: old and new algorithms}},
  booktitle =	{Numerical Methods for Structured Markov Chains},
  pages =	{1--28},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7461},
  editor =	{Dario Bini and Beatrice Meini and Vaidyanathan Ramaswami and Marie-Ange Remiche and Peter Taylor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.07461.7},
  URN =		{urn:nbn:de:0030-drops-13987},
  doi =		{10.4230/DagSemProc.07461.7},
  annote =	{Keywords: Algebraic Riccati Equation, Matrix Equation, Cyclic Reduction, Structured doubling algorithm}
}
Document
DOI: 10.4230/DagSemProc.07461.11
Nonsymmetric algebraic Riccati equations associated with an M-matrix: recent advances and algorithms

Authors: Dario A. Bini, Bruno Iannazzo, Beatrice Meini, and Federico Poloni

Published in: Dagstuhl Seminar Proceedings, Volume 7461, Numerical Methods for Structured Markov Chains (2008)

Abstract
We survey on theoretical properties and algorithms concerning the problem of solving a nonsymmetric algebraic Riccati equation, and we report on some known methods and new algorithmic advances. In particular, some results on the number of positive solutions are proved and a careful convergence analysis of Newton's iteration is carried out in the cases of interest where some singularity conditions are encountered. From this analysis we determine initial approximations which still guarantee the quadratic convergence.
Cite as

Dario A. Bini, Bruno Iannazzo, Beatrice Meini, and Federico Poloni. Nonsymmetric algebraic Riccati equations associated with an M-matrix: recent advances and algorithms. In Numerical Methods for Structured Markov Chains. Dagstuhl Seminar Proceedings, Volume 7461, pp. 1-31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{bini_et_al:DagSemProc.07461.11,
  author =	{Bini, Dario A. and Iannazzo, Bruno and Meini, Beatrice and Poloni, Federico},
  title =	{{Nonsymmetric algebraic Riccati equations associated with an M-matrix: recent advances and algorithms}},
  booktitle =	{Numerical Methods for Structured Markov Chains},
  pages =	{1--31},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7461},
  editor =	{Dario Bini and Beatrice Meini and Vaidyanathan Ramaswami and Marie-Ange Remiche and Peter Taylor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.07461.11},
  URN =		{urn:nbn:de:0030-drops-13958},
  doi =		{10.4230/DagSemProc.07461.11},
  annote =	{Keywords: Nonsymmetric algebraic Riccati equations, matrix equation, M-matrices, Newton method, quadratically convergent algorithms, cyclic reduction, doubling}
}
Document
DOI: 10.4230/DagSemProc.07461.13
On the tail decay of M/G/1-type Markov renewal processes

Authors: Dario A. Bini, Beatrice Meini, and Vaidyanathan Ramaswami

Published in: Dagstuhl Seminar Proceedings, Volume 7461, Numerical Methods for Structured Markov Chains (2008)

Abstract
The tail decay of M/G/1-type Markov renewal processes is studied. The Markov renewal process is transformed into a Markov chain so that the problem of tail decay is reformulated in terms of the decay of the coefficients of a suitable power series. The latter problem is reduced to analyze the analyticity domain of the power series.
Cite as

Dario A. Bini, Beatrice Meini, and Vaidyanathan Ramaswami. On the tail decay of M/G/1-type Markov renewal processes. In Numerical Methods for Structured Markov Chains. Dagstuhl Seminar Proceedings, Volume 7461, pp. 1-7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{bini_et_al:DagSemProc.07461.13,
  author =	{Bini, Dario A. and Meini, Beatrice and Ramaswami, Vaidyanathan},
  title =	{{On the tail decay of M/G/1-type Markov renewal processes}},
  booktitle =	{Numerical Methods for Structured Markov Chains},
  pages =	{1--7},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7461},
  editor =	{Dario Bini and Beatrice Meini and Vaidyanathan Ramaswami and Marie-Ange Remiche and Peter Taylor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.07461.13},
  URN =		{urn:nbn:de:0030-drops-13966},
  doi =		{10.4230/DagSemProc.07461.13},
  annote =	{Keywords: Renewal processes, tail decay, M/G/1-type Markov chains}
}
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