广义Rybicki Press算法
Generalized Rybicki Press algorithm
摘要：
本文讨论了一个更一般的和数值稳定的Rybicki Press算法，它能够求逆和计算协方差阵的行列式，其元素是指数和。该算法是正确的，在精确的算术和依赖于引入新的变量和相应的方程，从而转换成一个带状矩阵的更大的大小。用于求解线性系和计算较大矩阵上的行列式的线性复杂度带状算法也使初始半可分矩阵的线性复杂度算法成为可能。提供的基准说明了算法的线性缩放。
英文摘要：
This article discusses a more general and numerically stable Rybicki Press algorithm, which enables inverting and computing determinants of covariance matrices, whose elements are sums of exponentials. The algorithm is true in exact arithmetic and relies on introducing new variables and corresponding equations, thereby converting the matrix into a banded matrix of larger size. Linear complexity banded algorithms for solving linear systems and computing determinants on the larger matrix enable linear complexity algorithms for the initial semi-separable matrix as well. Benchmarks provided illustrate the linear scaling of the algorithm.
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。
