最优多边形L1线性化及非线性系统的快速插值
Optimal polygonal L1 linearization and fast interpolation of nonlinear systems
AI总结：
本文提出一种基于L1范数的多边形模型，用于高效线性化和插值非线性系统，通过误差分析优化多边形近似设计，适用于GPU实现的实时计算。
摘要：
复杂非线性系统的分析通常使用更简单的分段线性表示。本文提出了一种原理性且实用的技术，用于使用多边形（连续分段线性）模型在L1范数下线性化和评估任意连续非线性函数。开发了详尽的误差分析，以指导在大预算评估子区间N的渐进行情下两种多边形近似的最优设计。该方法允许用户根据目标近似误差获得线性化级别（N），反之亦然。它适用于但不仅限于在现代图形处理单元（GPU）上的高效实现，允许计算密集型应用的实时性能。该技术的质量和效率已在两个广泛用于许多科学计算领域且计算成本较高的非线性函数上进行了详细测量。
英文摘要：
The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using polygonal (continuous piecewise linear) models under the L1 norm. A thorough error analysis is developed to guide an optimal design of two kinds of polygonal approximations in the asymptotic case of a large budget of evaluation subintervals N. The method allows the user to obtain the level of linearization (N) for a target approximation error and vice versa. It is suitable for, but not limited to, an efficient implementation in modern Graphics Processing Units (GPUs), allowing real-time performance of computationally demanding applications. The quality and efficiency of the technique has been measured in detail on two nonlinear functions that are widely used in many areas of scientific computing and are expensive to evaluate
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。
