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Generalized Reflection Coefficients in Toeplitz-Block-Toeplitz Matrix Case and Fast Inverse 2D levinson Algorithm

Rami Kanhouche

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Abstract

A factorization of the inverse of a Hermetian positive definite matrix based on a diagonal by diagonal recurrence formulae permits the inversion of Toeplitz Block Toeplitz matrices using minimized matrix-vector products, with a complexity of ((n1)^3)((n2)^2), where n1 is the block size, and n2 is the block matrix size. A 2D levinson algorithm is introduced that outperform Wittle, Wiggins and Robinson Algorithm

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A factorization of the inverse of a Hermetian positive definite matrix based on a diagonal by diagonal recurrence formulae permits the inversion of Toeplitz Block Toeplitz matrices using minimized matrix-vector products, with a complexity of ((n1)^3)((n2)^2), where n1 is the block size, and n2 is the block matrix size. A 2D levinson algorithm is introduced that outperform Wittle, Wiggins and Robinson Algorithm

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Available abstract

A factorization of the inverse of a Hermetian positive definite matrix based on a diagonal by diagonal recurrence formulae permits the inversion of Toeplitz Block Toeplitz matrices using minimized matrix-vector products, with a complexity of ((n1)^3)((n2)^2), where n1 is the block size, and n2 is the block matrix size. A 2D levinson algorithm is introduced that outperform Wittle, Wiggins and Robinson Algorithm

Key concepts: Toeplitz matrix, Levinson recursion, Inverse, Block (permutation group theory), Algorithm, Mathematics, Matrix (chemical analysis), Reflection (computer programming)

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Generalized Reflection Coefficients in Toeplitz-Block-Toeplitz Matrix Case and Fast Inverse 2D levinson Algorithm — Research Paper | ScholarLens