论文标题
张量线性系统的随机kaczmarz
Randomized Kaczmarz for Tensor Linear Systems
论文作者
论文摘要
求解方程式的线性系统是数学中的基本问题。当线性系统如此之大以至于无法立即将其加载到内存中时，诸如随机Kaczmarz方法Excel之类的迭代方法Excel。在这里，我们扩展了随机的kaczmarz方法，以求解张量tensor t-product的多线性（张量）系统。我们为提出的张量随机kaczmarz提供收敛保证，这些kaczmarz类似于矩阵线性系统的随机kaczmarz方法。我们在实验上证明，张量随机kaczmarz方法比传统的随机kaczmarz收敛的速度更快，该kaczmarz应用于线性系统的天真添加版本。此外，我们在拟议的算法和用于基质线性系统的随机Kaczmarz算法的先前已知扩展之间进行了连接。
Solving linear systems of equations is a fundamental problem in mathematics. When the linear system is so large that it cannot be loaded into memory at once, iterative methods such as the randomized Kaczmarz method excel. Here, we extend the randomized Kaczmarz method to solve multi-linear (tensor) systems under the tensor-tensor t-product. We provide convergence guarantees for the proposed tensor randomized Kaczmarz that are analogous to those of the randomized Kaczmarz method for matrix linear systems. We demonstrate experimentally that the tensor randomized Kaczmarz method converges faster than traditional randomized Kaczmarz applied to a naively matricized version of the linear system. In addition, we draw connections between the proposed algorithm and a previously known extension of the randomized Kaczmarz algorithm for matrix linear systems.
