Numerical Simulations of General Markov Random Fields Using Biorthonormal Transfer-Matrix Renormalization-Group Method
碩士 === 南榮科技大學 === 工程科技研究所碩士班 === 103 === We seek numerical calculations of partition functions of general Markov random fields (MRFs) by using the biorthonormal transfer-matrix renormalization-group (BTMRG) method. The BTMRG is a modification of the conventional TMRG, a variant of the density-matrix...
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ndltd-TW-103NJI000290162017-02-19T04:30:38Z http://ndltd.ncl.edu.tw/handle/08119843640296664980 Numerical Simulations of General Markov Random Fields Using Biorthonormal Transfer-Matrix Renormalization-Group Method 雙正交轉移矩陣重整群於廣義馬可夫隨機場之 數值模擬 Chih-Hao Peng 彭志豪 碩士 南榮科技大學 工程科技研究所碩士班 103 We seek numerical calculations of partition functions of general Markov random fields (MRFs) by using the biorthonormal transfer-matrix renormalization-group (BTMRG) method. The BTMRG is a modification of the conventional TMRG, a variant of the density-matrix renormalization-group (DMRG), which automatically truncates the Hilbert space so that the properties of large systems can be precisely calculated while the dimensions of the renormalized transfer matrix remain constant. We apply the BTMRG to the decimation of the fundamental transfer matrix for general MRFs. Four binary 2nd-order MRFs are selected for numerical simulations. Results of simulations show that all four models exhibit the phase transition phenomenon. This work also shows that our BTMRG method is superior to the conventional TMRG in accuracy, computational speed, and in the possibility of treating a much larger system. Yu-Kun Huang 黃玉坤 2015 學位論文 ; thesis 88 zh-TW |
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碩士 === 南榮科技大學 === 工程科技研究所碩士班 === 103 === We seek numerical calculations of partition functions of general Markov random fields (MRFs) by using the biorthonormal transfer-matrix renormalization-group (BTMRG) method. The BTMRG is a modification of the conventional TMRG, a variant of the density-matrix renormalization-group (DMRG), which automatically truncates the Hilbert space so that the properties of large systems can be precisely calculated while the dimensions of the renormalized transfer matrix remain constant. We apply the BTMRG to the decimation of the fundamental transfer matrix for general MRFs. Four binary 2nd-order MRFs are selected for numerical simulations. Results of simulations show that all four models exhibit the phase transition phenomenon. This work also shows that our BTMRG method is superior to the conventional TMRG in accuracy, computational speed, and in the possibility of treating a much larger system.
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author2 |
Yu-Kun Huang |
author_facet |
Yu-Kun Huang Chih-Hao Peng 彭志豪 |
author |
Chih-Hao Peng 彭志豪 |
spellingShingle |
Chih-Hao Peng 彭志豪 Numerical Simulations of General Markov Random Fields Using Biorthonormal Transfer-Matrix Renormalization-Group Method |
author_sort |
Chih-Hao Peng |
title |
Numerical Simulations of General Markov Random Fields Using Biorthonormal Transfer-Matrix Renormalization-Group Method |
title_short |
Numerical Simulations of General Markov Random Fields Using Biorthonormal Transfer-Matrix Renormalization-Group Method |
title_full |
Numerical Simulations of General Markov Random Fields Using Biorthonormal Transfer-Matrix Renormalization-Group Method |
title_fullStr |
Numerical Simulations of General Markov Random Fields Using Biorthonormal Transfer-Matrix Renormalization-Group Method |
title_full_unstemmed |
Numerical Simulations of General Markov Random Fields Using Biorthonormal Transfer-Matrix Renormalization-Group Method |
title_sort |
numerical simulations of general markov random fields using biorthonormal transfer-matrix renormalization-group method |
publishDate |
2015 |
url |
http://ndltd.ncl.edu.tw/handle/08119843640296664980 |
work_keys_str_mv |
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