面向宇宙微波背景空间源分离的Sylvester结构系统的快速求解
Fast solution of Sylvester-structured systems for spatial source separation of the Cosmic Microwave Background
AI总结：
本文提出使用Krylov子空间方法解决宇宙学源分离中大规模Sylvester结构线性系统的求解瓶颈，通过共轭梯度法和Sylvester矩阵方程重构两种途径，在合理计算时间和内存下实现了准确求解。
摘要：
实现许多用于大型多元数据集的统计方法需要求解一个线性系统，该系统根据方法不同，其维度取决于观测数量或每个单独数据向量的维度。这通常是限制方法随数据规模和复杂性扩展的瓶颈。本文展示了使用Krylov子空间方法来解决宇宙学中源分离问题的统计解算中的此问题，该问题的数据规模过大，无法直接求解所需系统。我们描述了两种改编自文献技术的不同方法：一种将共轭梯度法直接应用于Kronecker结构问题，另一种将系统重新表述为Sylvester矩阵方程。我们表明，对于当前可用的数据规模，两种方法均能在可接受的计算时间内并以实用的内存需求产生准确的解。
英文摘要：
Implementation of many statistical methods for large, multivariate data sets requires one to solve a linear system that, depending on the method, is of the dimension of the number of observations or each individual data vector. This is often the limiting factor in scaling the method with data size and complexity. In this paper we illustrate the use of Krylov subspace methods to address this issue in a statistical solution to a source separation problem in cosmology where the data size is prohibitively large for direct solution of the required system. Two distinct approaches, adapted from techniques in the literature, are described: one that uses the method of conjugate gradients directly to the Kronecker-structured problem and another that reformulates the system as a Sylvester matrix equation. We show that both approaches produce an accurate solution within an acceptable computation time and with practical memory requirements for the data size that is currently available.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
