Solving block-banded block Toeplitz systems with banded Toeplitz blocks

Details Solving block-banded block Toeplitz systems with banded Toeplitz blocks Solving block-banded block Toeplitz systems with banded Toeplitz blocks

Nov 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999spie.3807..300b&link_type=abstract

Proc. SPIE Vol. 3807, p. 300-311, Advanced Signal Processing Algorithms, Architectures, and Implementations IX, Franklin T. Luk;

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Scientific paper

We introduce the concept of (epsilon) -displacement rank, that allows us to devise a fast algorithm for the approximate solution of BBBT/BTB (Block Banded Block Toeplitz with Banded Toeplitz Blocks) systems by means of cyclic reduction. We also introduce the concept of incomplete displacement block LU factorization of a Toeplitz-like matrix, where the displacement structure is imposed to the blocks of the factors L and U. The role of the matrix LU as preconditioner is discussed. Finally we propose another preconditioner obtained by extending a BBBT/BTB matrix to a banded Toeplitz matrix. Some open problems are addressed.

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