@article{b08cef5d8c3e475f8589f88ecc213289,
title = "Integer Levinson Algorithm for the Inversion of Any Nonsingular Hermitian Toeplitz Matrix",
abstract = "This paper presents an integer preserving (IP) version of the Levinson algorithm to solve a normal set of equations for a Hermitian Toeplitz matrix with any singularity profile. The IP property means that for a matrix with integer entries, the algorithm can be completed over the integer solely by using a ring of integer operations. The IP algorithm provides remedies for unpredictable numerical outcomes when a corresponding floating-point (FP) Levinson algorithm either overlooks zero principal minors (PMs) or applies a singularity skipping routine to a PM that is considered erroneously to be zero. The error-free computational edge of integer arithmetic is also applicable to a non-integer Toeplitz matrix by first scaling it up to an acceptably accurate integer matrix. The proposed algorithm can also be used to obtain the inverse of a nonsingular Hermitian Toeplitz matrix (with any singularity profile) by one of two proposed IP Gohberg-Semencul type inversion formulas.",
keywords = "Gohberg-Semencul inversion formulas, Levinson algorithms, Toeplitz matrices, integer algorithms",
author = "Yuval Bistritz and Idan Dekel",
note = "Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",
year = "2024",
month = apr,
day = "1",
doi = "10.1109/TIT.2024.3364574",
language = "אנגלית",
volume = "70",
pages = "3018--3031",
journal = "IEEE Transactions on Information Theory",
issn = "0018-9448",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "4",
}