论文标题
偏斜矩阵乘法
Skew-sparse matrix multiplication
论文作者
论文摘要
基于这样的观察，即$ \ mathbb {q}^{（p-1）\ times（p-1）} $对商的偏度多项式戒指是同构的，我们为$（p-1）\ times（p-1）\ times（p-1）$ matrix乘以$ \ mathbb {q} $ p $ p $ p $ p $ ys py-is proull yrume yriles yriles proumple yriles yriles yrume ys proulms ys Proumple。我们方法的主要特征是如果产品是偏斜的，则矩阵乘法的加速度。基于新方法，我们设计了一种具有复杂性$ o（t^{ω-2} p^2）$的确定性算法，其中$ t \ le p-1 $是输入矩阵的偏心和$ω$确定的参数，而$ω$是矩阵乘法的渐近指数。此外，通过引入随机性，我们还提出了一种具有复杂性的概率算法$ o^\ thumSim（t^{ω-2} p^2+p^2+p^2 \ log \ frac {1}ν）$，其中$ t \ le p-1 $是产品和$ $ $ $ compars的skew-sparsity。
Based on the observation that $\mathbb{Q}^{(p-1) \times (p-1)}$ is isomorphic to a quotient skew polynomial ring, we propose a new method for $(p-1)\times (p-1)$ matrix multiplication over $\mathbb{Q}$, where $p$ is a prime number. The main feature of our method is the acceleration for matrix multiplication if the product is skew-sparse. Based on the new method, we design a deterministic algorithm with complexity $O(T^{ω-2} p^2)$, where $T\le p-1$ is a parameter determined by the skew-sparsity of input matrices and $ω$ is the asymptotic exponent of matrix multiplication. Moreover, by introducing randomness, we also propose a probabilistic algorithm with complexity $O^\thicksim(t^{ω-2}p^2+p^2\log\frac{1}ν)$, where $t\le p-1$ is the skew-sparsity of the product and $ν$ is the probability parameter.
