@Article{NMTMA-2-469,
author = {Ichitaro Yamazaki, Zhaojun Bai, Wenbin Chen and Richard Scalettar},
title = {A High-Quality Preconditioning Technique for Multi-Length-Scale Symmetric Positive Definite Linear Systems},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2009},
volume = {2},
number = {4},
pages = {469--484},
abstract = {<p style="text-align: justify;">We study preconditioning techniques used in conjunction with the conjugate
gradient method for solving multi-length-scale symmetric positive definite linear systems originating from the quantum Monte Carlo simulation of electron interaction of
correlated materials. Existing preconditioning techniques are not designed to be adaptive to varying numerical properties of the multi-length-scale systems. In this paper,
we propose a hybrid incomplete Cholesky (HIC) preconditioner and demonstrate its
adaptivity to the multi-length-scale systems. In addition, we propose an extension of
the compressed sparse column with row access (CSCR) sparse matrix storage format to
efficiently accommodate the data access pattern to compute the HIC preconditioner. We
show that for moderately correlated materials, the HIC preconditioner achieves the optimal linear scaling of the simulation. The development of a linear-scaling preconditioner
for strongly correlated materials remains an open topic.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2009.m9008s},
url = {http://global-sci.org/intro/article_detail/nmtma/6036.html}
}