Recent advances in rigorous computation of Poincaré maps

具有多个时滞的时滞微分方程组中 Poincaré 映射严格计算的高阶 Lohner 型算法

High-order Lohner-type algorithm for rigorous computation of Poincaré maps in systems of Delay Differential Equations with several delays

提出一种用于多时滞时滞微分方程严格积分的高阶 Lohner 型算法，基于解的分段 Taylor 表示与平滑特性计算 Poincaré 映射，并结合拓扑技术证明了 Mackey-Glass 方程和 Rössler 系统中的复杂动力学行为。

Rigorous Roundoff Error Analysis of Probabilistic Floating-Point Computations

We present a detailed study of roundoff errors in probabilistic floating-point computations. We derive closed-form expressions for the distribution of roundoff errors associated with a random variable, and we prove that roundoff errors are generally close to being uncorrelated with their generating distribution. Based on these theoretical advances, we propose a model of IEEE floating-point arithmetic for numerical expressions with probabilistic inputs and an algorithm for evaluating this model. Our algorithm provides rigorous bounds to the output and error distributions of arithmetic expressio…