论文标题
通过类似Lanczos的方法，具有可变系数的耦合线性微分方程的系统的三角法化
Tridiagonalization of systems of coupled linear differential equations with variable coefficients by a Lanczos-like method
论文作者
论文摘要
我们建设性地表明，在某些规律性假设下，具有可变系数的任何耦合线性微分方程系统都可以通过类似时间的Lanczos样方法进行三型分子化。我们提供的证据正式建立了类似Lanczos的算法的收敛性，并产生了算法分解的完整表征。从那里，原始差分系统的解决方案以封闭形式可用。这是正式和数值评估难以捉摸的有序指数函数的关键部分。
We show constructively that, under certain regularity assumptions, any system of coupled linear differential equations with variable coefficients can be tridiagonalized by a time-dependent Lanczos-like method. The proof we present formally establishes the convergence of the Lanczos-like algorithm and yields a full characterization of algorithmic breakdowns. From there, the solution of the original differential system is available in closed form. This is a key piece in evaluating the elusive ordered exponential function both formally and numerically.
