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Journal Articles IEEE Transactions on Computers Year : 2013

Multiway Splitting Method for Toeplitz Matrix Vector Product

Abstract

Computing the product of a Toeplitz matrix and a vector arises in various applications including cryptography. In this paper, we consider Toeplitz matrices and vectors with entries in $({hbox{rlap{I}kern 2.0pt{hbox{F}}}}_2)$. For improved efficiency in such computations, large Toeplitz matrices and vectors are recursively split and special formulas with subquadratic arithmetic complexity are applied. To this end, we first present a formula for the five-way splitting and then provide a generalization for the $(k)$-way splitting, where $(k)$ is an arbitrary integer. These formulas can be used to compute a Toeplitz matrix-vector product (TMVP) of size $(n)$ with an arithmetic complexity of $(O(n^{log_k(k(k+1)/2)}))$.
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Dates and versions

hal-00839952 , version 1 (01-07-2013)

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Anwar Hasan, Christophe Negre. Multiway Splitting Method for Toeplitz Matrix Vector Product. IEEE Transactions on Computers, 2013, 62 (7), pp.1467-1471. ⟨10.1109/TC.2012.95⟩. ⟨hal-00839952⟩
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