Solving block-banded block Toeplitz systems with banded Toeplitz blocks

Dario Andrea Bini; Beatrice Meini

doi:10.1117/12.367646

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

Dario Andrea Bini, Beatrice Meini

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.

Citation Download Citation

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

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available