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Multiway Splitting Method for Toeplitz Matrix Vector Product
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DOI：10.1109/TC.2012.95.png)
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摘要
En 中文
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 IF2. 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(logk) ((k(k+1)/2))).
Keyword:
Toeplitz matrix vector product
subquadratic complexity
parallel multiplier
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