论文标题
部分可观测时空混沌系统的无模型预测
Fast algorithms for least square problems with Kronecker lower subsets
论文作者
论文摘要
虽然杠杆得分采样提供了强大的工具，可用于近似最小二乘问题的解决方案，但计算精确得分和抽样的成本通常禁止使用实际应用。本文通过开发一种适用于Kronecker产品矩阵较低列子集的矩阵的精确杠杆评分采样来解决这一挑战。我们合成相关的近似保证并详细说明了专门利用此结构属性的算法来达到计算效率。通过数值示例，我们证明，与确定的近似近似杠杆得分采样策略相比，通过我们的方法有效计算的精确杠杆得分会大大减少近似误差。
While leverage score sampling provides powerful tools for approximating solutions to large least squares problems, the cost of computing exact scores and sampling often prohibits practical application. This paper addresses this challenge by developing a new and efficient algorithm for exact leverage score sampling applicable to matrices that are lower column subsets of Kronecker product matrices. We synthesize relevant approximation guarantees and detail the algorithm that specifically leverages this structural property for computational efficiency. Through numerical examples, we demonstrate that utilizing efficiently computed exact leverage scores via our methods significantly reduces approximation errors, as compared to established approximate leverage score sampling strategies when applied to this important class of structured matrices.
