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arXiv 2304.04458astro-ph.EPastro-ph.IMphysics.comp-ph
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行星历表数值积分中舍入误差的减少

Reducing roundoff errors in numerical integration of planetary ephemeris

Maxim Subbotin, Alexander Kodukov, Dmitry Pavlov

AI总结:

针对长跨度行星历表数值积分中累积舍入误差超过高精度观测随机误差的问题,提出使用double-double算术替代扩展精度算术,以在保持双精度浮点原语普遍支持的同时减少误差。

摘要:

现代月球-行星历表的数值积分在超过100年的观测时间跨度上进行(其中最近20年具有极高精度的天体测量数据)。在如此长的时间跨度上,不仅有限差分近似误差,而且累积的算术舍入误差也变得重要,因为它们超过了月球、火星和水星的高精度测距观测值的随机误差。解决此问题的一种方法是使用x86处理器上可用的扩展精度算术。注意到该方法的缺点,我们提出了一种替代方案:在适当的地方使用double-double算术。这将允许仅使用具有普遍支持的双精度浮点原语。

英文摘要:

Modern lunar-planetary ephemerides are numerically integrated on the observational timespan of more than 100 years (with the last 20 years having very precise astrometrical data). On such long timespans, not only finite difference approximation errors, but also the accumulating arithmetic roundoff errors become important because they exceed random errors of high-precision range observables of Moon, Mars, and Mercury. One way to tackle this problem is using extended-precision arithmetics available on x86 processors. Noting the drawbacks of this approach, we propose an alternative: using double-double arithmetics where appropriate. This will allow to use only double precision floating-point primitives which have ubiquitous support.

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。

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