An Algorithm for Solving Systems of Quadratic Equations in Branching Processes

Federico Poloni

Bollettino dell'Unione Matematica Italiana (2013)

  • Volume: 6, Issue: 2, page 481-486
  • ISSN: 0392-4041

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Poloni, Federico. "An Algorithm for Solving Systems of Quadratic Equations in Branching Processes." Bollettino dell'Unione Matematica Italiana 6.2 (2013): 481-486. <http://eudml.org/doc/294046>.

@article{Poloni2013,
author = {Poloni, Federico},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {481-486},
publisher = {Unione Matematica Italiana},
title = {An Algorithm for Solving Systems of Quadratic Equations in Branching Processes},
url = {http://eudml.org/doc/294046},
volume = {6},
year = {2013},
}

TY - JOUR
AU - Poloni, Federico
TI - An Algorithm for Solving Systems of Quadratic Equations in Branching Processes
JO - Bollettino dell'Unione Matematica Italiana
DA - 2013/6//
PB - Unione Matematica Italiana
VL - 6
IS - 2
SP - 481
EP - 486
LA - eng
UR - http://eudml.org/doc/294046
ER -

References

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  1. BEAN, N. G. - KONTOLEON, N. - TAYLOR, P. G., Markovian trees: properties and algorithms, Ann. Oper. Res., 160 (2008), 31-50. Zbl1213.60133MR2396636DOI10.1007/s10479-007-0295-9
  2. BINI, D. A. - MEINI, B. - POLONI, F., On the solution of a quadratic vector equation arising in Markovian binary trees, Numer. Linear Algebra Appl., 18, n. 6 (2011), 981-991. Zbl1265.65105MR2861273DOI10.1002/nla.809
  3. HAUTPHENNE, S. - LATOUCHE, G. - REMICHE, M.-A., Algorithmic Approach to the Extinction Probability of Branching Processes, Methodology and Computing in Applied Probability (2010). MR2755138DOI10.1007/s11009-009-9141-7
  4. HAUTPHENNE, S. - LATOUCHE, G. - REMICHE, M.-A., Newton's iteration for the extinction probability of a Markovian binary tree, Linear Algebra Appl., 428 (11- 12) (2008), 2791-2804. MR2416589DOI10.1016/j.laa.2007.12.024
  5. HAUTPHENNE, S. - LEIBNITZ, K. - REMICHE, M.-A., Modeling of P2P file sharing with a level-dependent QBD process, Advances in queueing theory and network applications, (Springer, New York, 2009), 247-263. MR2768441DOI10.1007/978-0-387-09703-9_14
  6. HAUTPHENNE, S. - VAN HOUDT, B., On the link between Markovian trees and tree-structured Markov chains, European Journal of Operational Research, 201, n. 3 (2010), 791-798. Zbl1173.90580MR2552497DOI10.1016/j.ejor.2009.03.052
  7. MEINI, B. - POLONI, F., A Perron iteration for the solution of a quadratic vector equation arising in Markovian binary trees, SIAM J. Matrix Anal. Appl., 32, n. 1 (2011), 248-261. Zbl1242.65104MR2811299DOI10.1137/100796765
  8. POLONI, F., Algorithms for quadratic matrix and vector equations, Vol. 16, Tesi. Scuola Normale Superiore di Pisa (Nuova Serie) [Theses of Scuola Normale Superiore di Pisa (New Series)], Dissertation, Scuola Normale Superiore, Pisa, 2011, pp. xvi+239. MR2840249DOI10.1007/978-88-7642-384-0
  9. POLONI, F., Quadratic vector equations, Linear Algebra and its Applications, Vol. 438, n. 4 (2013), 1627-1644 (https://www.sciencedirect.com/science/article/pii/S0024379511004484?np=y). Zbl1268.15014

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