Solving block-banded block Toeplitz systems with banded Toeplitz blocks

Dario Andrea Bini; Beatrice Meini

doi:10.1117/12.367646

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2 November 1999 Solving block-banded block Toeplitz systems with banded Toeplitz blocks

Dario Andrea Bini; Beatrice Meini

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Proceedings Volume 3807, Advanced Signal Processing Algorithms, Architectures, and Implementations IX; (1999) https://doi.org/10.1117/12.367646
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

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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Dario Andrea Bini and Beatrice Meini "Solving block-banded block Toeplitz systems with banded Toeplitz blocks", Proc. SPIE 3807, Advanced Signal Processing Algorithms, Architectures, and Implementations IX, (2 November 1999); https://doi.org/10.1117/12.367646

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