TY - JOUR
T1 - Circulant preconditioners for toeplitz matrices with positive continuous generating functions
AU - CHAN, Raymond H.
AU - YEUNG, Man Chung
PY - 1992/1
Y1 - 1992/1
N2 - We consider the solution of n-by-n Toeplitz systems Anx = b by the preconditioned conjugate gradient method. The preconditioner Cn is the circulant matrix that minimizes ∥Bn − An∥F over all circulant matrices Bn. We show that if the generating function f is a positive 2π-periodic continuous function, then the spectrum of the preconditioned system Cn−1 An will be clustered around one. In particular, if the preconditioned conjugate gradient method is applied to solve the preconditioned system, the convergence rate is superlinear.
AB - We consider the solution of n-by-n Toeplitz systems Anx = b by the preconditioned conjugate gradient method. The preconditioner Cn is the circulant matrix that minimizes ∥Bn − An∥F over all circulant matrices Bn. We show that if the generating function f is a positive 2π-periodic continuous function, then the spectrum of the preconditioned system Cn−1 An will be clustered around one. In particular, if the preconditioned conjugate gradient method is applied to solve the preconditioned system, the convergence rate is superlinear.
UR - http://www.scopus.com/inward/record.url?scp=84968515314&partnerID=8YFLogxK
U2 - 10.1090/S0025-5718-1992-1106960-1
DO - 10.1090/S0025-5718-1992-1106960-1
M3 - Journal Article (refereed)
AN - SCOPUS:84968515314
SN - 0025-5718
VL - 58
SP - 233
EP - 240
JO - Mathematics of Computation
JF - Mathematics of Computation
IS - 197
ER -