Circulant preconditioners from B-splines

Raymond Hon-fu Chan; Tat-Ming Tso; Hai-wai Sun

doi:10.1117/12.284188

24 October 1997 Circulant preconditioners from B-splines

Raymond Hon-fu Chan, Tat-Ming Tso, Hai-wai Sun

Proceedings Volume 3162, Advanced Signal Processing: Algorithms, Architectures, and Implementations VII; (1997) https://doi.org/10.1117/12.284188
Event: Optical Science, Engineering and Instrumentation '97, 1997, San Diego, CA, United States

Abstract

In this paper, we propose a new family of circulant preconditioners for solving Toeplitz systems. They are based on B-splines. The R. Chan and T. Chan preconditioners can be constructed from the first and the second order B-splines. Numerical results show that preconditioners from higher-order B-splines perform much better than well-known ones even in the cases where the Toeplitz matrices are ill-conditioned. Like that of the other circulant preconditioners, the construction of B-spline preconditioners requires only the entries of the given Toeplitz matrix and does not require an a priori knowledge of its generating function. Thus they are most suitable for applications where the generating function of the given Toeplitz matrix is not known explicitly.

Citation Download Citation

Raymond Hon-fu Chan, Tat-Ming Tso, and Hai-wai Sun "Circulant preconditioners from B-splines", Proc. SPIE 3162, Advanced Signal Processing: Algorithms, Architectures, and Implementations VII, (24 October 1997); https://doi.org/10.1117/12.284188

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