caa a22 4500 463171667 CHVBK 20180406164815.0 cr unu---uuuuu 170326e20070301xx s 000 0 eng 10.1007/s-10998-007-1107-3 doi (NATIONALLICENCE)springer-10.1007/s-10998-007-1107-3 Éltető Tamás Traffic Lab, Ericsson, Hungary aut Why certain discrete phase type representations have numerically stable spectral decomposition [Elektronische Daten] [Tamás Éltető] The discrete-time phase type (PH) distributions are used in the numerical solution of many problems. The representation of a PH distribution consists of a vector and a substochastic matrix. The common feature of the PH distributions is that they have rational moment generating function. The moment generating function depends on the eigendecomposition of the transition probability matrix of the PH distribution, but the eigenvalues and eigenvectors are important in other cases as well. Due to the finite precision of the numerical calculations or other reasons, a representation may contain errors that change the eigendecomposition. This paper presents upper bounds on the change of the eigendecomposition when the PH representation is perturbed. Since these bounds do not depend on a particular representation, but they hold for all, the analysed PH representations have uniformly stable spectral decompositions. Akadémiai Kiadó, 2007 phase type representation nationallicence matrix perturbation nationallicence condition number nationallicence Periodica Mathematica Hungarica Kluwer Academic Publishers 54/1(2007-03-01), 107-120 0031-5303 54:1<107 2007 54 10998 https://doi.org/10.1007/s-10998-007-1107-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s-10998-007-1107-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Éltető Tamás Traffic Lab, Ericsson, Hungary aut NATIONALLICENCE 773 0- Periodica Mathematica Hungarica Kluwer Academic Publishers 54/1(2007-03-01), 107-120 0031-5303 54:1<107 2007 54 10998 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer