Characterizing the inverses of block tridiagonal, block Toeplitz matrices

Boffi, Nicholas M.; Hill, Judith C.; Reuter, Matthew G.

doi:10.1088/1749-4680/8/1/015001

Title: Characterizing the inverses of block tridiagonal, block Toeplitz matrices

Journal Article · Thu Jan 01 00:00:00 EST 2015 · Computational Science and Discovery

DOI:https://doi.org/10.1088/1749-4680/8/1/015001· OSTI ID:1567555

Boffi, Nicholas M. ^[1]; Hill, Judith C. ^[2]; Reuter, Matthew G. ^[3]

Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Center for Nanophase Materials Science (CNMS)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). National Center for Computational Sciences
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science & Mathematics Division

We consider the inversion of block tridiagonal, block Toeplitz matrices and comment on the behaviour of these inverses as one moves away from the diagonal. Using matrix Möbius transformations, we first present an O(1) representation (with respect to the number of block rows and block columns) for the inverse matrix and subsequently use this representation to characterize the inverse matrix. There are four symmetry-distinct cases where the blocks of the inverse matrix (i) decay to zero on both sides of the diagonal, (ii) oscillate on both sides, (iii) decay on one side and oscillate on the other and (iv) decay on one side and grow on the other. This characterization exposes the necessary conditions for the inverse matrix to be numerically banded and may also aid in the design of preconditioners and fast algorithms. Finally, we present numerical examples of these matrix types.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)

Sponsoring Organization:: USDOE Office of Science (SC), Workforce Development for Teachers and Scientists (WDTS)

DOE Contract Number:: AC05-00OR22725

OSTI ID:: 1567555

Journal Information:: Computational Science and Discovery, Vol. 8, Issue 1; ISSN 1749-4699

Country of Publication:: United States

Language:: English

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