1. Algebra of L-Banded Matrices
- Author
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Shunqi Huang, Lei Liu, and Brian M. Kurkoski
- Subjects
L-banded matrices ,iterative variable estimation algorithms ,convergence ,optimized vector damping ,Electrical engineering. Electronics. Nuclear engineering ,TK1-9971 - Abstract
Convergence is a crucial issue in iterative algorithms. Damping is commonly employed to ensure the convergence of iterative algorithms. The conventional ways of damping are scalar-wise, and either heuristic or empirical. Recently, an analytically optimized vector damping was proposed for memory message-passing (iterative) algorithms. As a result, it yields a special class of covariance matrices called L-banded matrices. In this paper, we show these matrices have broad algebraic properties arising from their L-banded structure. In particular, compact analytic expressions for the LDL decomposition, the Cholesky decomposition, the determinant after a column substitution, minors, and cofactors are derived. Furthermore, necessary and sufficient conditions for an L-banded matrix to be definite, a recurrence to obtain the characteristic polynomial, and some other properties are given.
- Published
- 2023
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