TY - GEN
T1 - Tiled Monte Carlo Algorithm
T2 - 2022 International Joint Conference on Information and Communication Engineering, JCICE 2022
AU - Choi, Hyeji
AU - Harrison, Robert J.
N1 - Publisher Copyright:
© 2022 IEEE.
PY - 2022
Y1 - 2022
N2 - While direct Monte Carlo (MC) algorithms are powerful tools for solving extremely large linear equations, the original MC algorithm is severely restricted in its applicability. We examine in detail the novel tiled MC linear algebra algorithm recently developed by us. The tiled algorithm, which samples a tile of the matrix instead of individual elements, was proven to converge for sufficiently large tile size. Random ma-trices and a matrix from chemical physics are used to explore and demonstrate the properties of the algorithm including the effect of tiling on both convergence and the statistical error, which in turn informs parameter selection. We also introduce and illustrate the use of practical numerical tools to assess convergence and the accuracy of computed statistics since the rigorous convergence test may not be readily computed for very large matrices.
AB - While direct Monte Carlo (MC) algorithms are powerful tools for solving extremely large linear equations, the original MC algorithm is severely restricted in its applicability. We examine in detail the novel tiled MC linear algebra algorithm recently developed by us. The tiled algorithm, which samples a tile of the matrix instead of individual elements, was proven to converge for sufficiently large tile size. Random ma-trices and a matrix from chemical physics are used to explore and demonstrate the properties of the algorithm including the effect of tiling on both convergence and the statistical error, which in turn informs parameter selection. We also introduce and illustrate the use of practical numerical tools to assess convergence and the accuracy of computed statistics since the rigorous convergence test may not be readily computed for very large matrices.
KW - Linear solver
KW - Monte Carlo algorithm
KW - Tiling
UR - https://www.scopus.com/pages/publications/85140902585
U2 - 10.1109/JCICE56791.2022.00049
DO - 10.1109/JCICE56791.2022.00049
M3 - Conference contribution
AN - SCOPUS:85140902585
T3 - Proceedings - 2022 International Joint Conference on Information and Communication Engineering, JCICE 2022
SP - 196
EP - 201
BT - Proceedings - 2022 International Joint Conference on Information and Communication Engineering, JCICE 2022
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 20 May 2022 through 22 May 2022
ER -