标题： 隐式重启Arnoldi方法在OFP8、Bfloat16、Posit和Takuma算术中的数值性能 显示英文标题

标题： Numerical Performance of the Implicitly Restarted Arnoldi Method in OFP8, Bfloat16, Posit, and Takum Arithmetics

摘要： 计算大型稀疏矩阵的选定特征值和特征向量对于广泛的应用至关重要。因此，评估新兴的替代IEEE 754浮点标准（如OFP8（E4M3和E5M2）、bfloat16以及渐进精度的posit和takum格式）的数值性能具有重要意义。在这个任务中最常用的方法之一是隐式重启Arnoldi方法，如ARPACK中的实现。本文基于两个真实世界的数据集进行了全面且未经调整的评估：SuiteSparse矩阵集合，其中包括不同大小和条件数的矩阵；以及网络仓库，这是一个来自实际应用的大规模图集合。结果显示，渐进精度的posit和takum格式提供了改进的数值性能，而takum算术避免了在posit中观察到的一些弱点。虽然bfloat16始终比float16表现更好，但OFP8类型通常不适合通用计算。 显示英文摘要

摘要： The computation of select eigenvalues and eigenvectors of large, sparse matrices is fundamental to a wide range of applications. Accordingly, evaluating the numerical performance of emerging alternatives to the IEEE 754 floating-point standard -- such as OFP8 (E4M3 and E5M2), bfloat16, and the tapered-precision posit and takum formats -- is of significant interest. Among the most widely used methods for this task is the implicitly restarted Arnoldi method, as implemented in ARPACK. This paper presents a comprehensive and untailored evaluation based on two real-world datasets: the SuiteSparse Matrix Collection, which includes matrices of varying sizes and condition numbers, and the Network Repository, a large collection of graphs from practical applications. The results demonstrate that the tapered-precision posit and takum formats provide improved numerical performance, with takum arithmetic avoiding several weaknesses observed in posits. While bfloat16 performs consistently better than float16, the OFP8 types are generally unsuitable for general-purpose computations.