TY - JOUR
T1 - Circulant Preconditioners for Elliptic Problems
AU - Chan, Raymond H.
AU - Chan, Tony F.
PY - 1992
Y1 - 1992
N2 - We propose and analyze the use of circulant preconditioners for the solution of elliptic problems via preconditioned iterative methods such as the conjugate gradient method Part of our motivation is to exploit the fast inversion of circulant systems via the Fast Fourier Transform FFT We prove that circulant preconditioners can be chosen so that the condition number of the preconditioned system can be reduced from O (n2) to O (n). Numerical experiments also indicatethat the preconditioned systems exhibit favorable clustering of eigen-values Both the computation based on averaging of the coecients of the elliptic operator and the inversion using FFTs of the circulantpreconditioners are highly parallelizable.
AB - We propose and analyze the use of circulant preconditioners for the solution of elliptic problems via preconditioned iterative methods such as the conjugate gradient method Part of our motivation is to exploit the fast inversion of circulant systems via the Fast Fourier Transform FFT We prove that circulant preconditioners can be chosen so that the condition number of the preconditioned system can be reduced from O (n2) to O (n). Numerical experiments also indicatethat the preconditioned systems exhibit favorable clustering of eigen-values Both the computation based on averaging of the coecients of the elliptic operator and the inversion using FFTs of the circulantpreconditioners are highly parallelizable.
UR - http://ftp.math.utah.edu/pub/tex/bib/toc/numlinaa.html#1(1):1992
UR - https://www.math.cuhk.edu.hk/~rchan/paper/elliptic.pdf
UR - http://repository.ust.hk/ir/Record/1783.1-49409
M3 - RGC 21 - Publication in refereed journal
VL - 1
SP - 77
EP - 101
JO - Numerical Linear Algebra with Applications
JF - Numerical Linear Algebra with Applications
SN - 1070-5325
IS - 1
ER -