Numerical Simulations of General Markov Random Fields Using Biorthonormal Transfer-Matrix Renormalization-Group Method

• Main Authors: Chih-Hao Peng, 彭志豪
• Other Authors: Yu-Kun Huang
• Format: Others
• Language: zh-TW
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/08119843640296664980

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.