Title: Randomized Methods for Large-Scale Linear Systems
Abstract: Solving linear systems is a crucial subroutine and challenge in data science and scientific computing. Classical approaches for solving linear systems assume that data is readily available and small enough to be stored in memory. However, in the large-scale data setting, data may be so large that only partitions (e.g., single rows/columns of the matrix/tensor) can be utilized at a time. In this presentation, we discuss the advantages and role of randomization in iterative methods for approximating the solution to large-scale linear systems. Time permitting, we will also discuss our recent work on applications to solving systems involving higher-dimensional arrays, or tensors. Unlike previously proposed randomized iterative strategies, such as the tensor randomized Kaczmarz method (row slice method) or the tensor Gauss-Seidel method (column slice method), which are natural extensions of their matrix counterparts, our approach delves into a distinct scenario utilizing frontal slice sketching.