## Computing the nearest reversible Markov chain

Please always quote using this URN: urn:nbn:de:0297-zib-53292

- Reversible Markov chains are the basis of many applications. However, computing transition probabilities by a finite sampling of a Markov chain can lead to truncation errors. Even if the original Markov chain is reversible, the approximated Markov chain might be non-reversible and will lose important properties, like the real valued spectrum. In this paper, we show how to find the closest reversible Markov chain to a given transition matrix. It turns out that this matrix can be computed by solving a convex minimization problem.

Author: | Adam Nielsen, Marcus Weber |
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Document Type: | ZIB-Report |

Tag: | Convex Optimization; MSM; Reversible Markov Chain |

MSC-Classification: | 15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY |

68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area) | |

Date of first Publication: | 2014/12/10 |

Series (Serial Number): | ZIB-Report (14-48) |

ISSN: | 1438-0064 |