Exploiting Structure in Floating-Point Arithmetic
Exploiting Structure in Floating-Point Arithmetic
复制标题
利用浮点运算中的结构
DOI：
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发表时间：
2015
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通讯作者：
C. Jeannerod
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文献类型：
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作者：
C. Jeannerod
IEEE浮点运算中的算法分析通常是通过重复应用所谓的标准模型来进行的，标准模型通过仅取决于格式的公共参数来限制每个基本操作的相对误差。虽然这种方法对于建立许多准确性和稳定性结果非常有用，但它无法捕获使浮点运算如此高度结构化的大多数低级功能。在本文中，我们调查的一些性质，以及如何利用它们在舍入误差分析。特别是，我们回顾了最近的一些改进的几个经典的，威尔金森式的误差界的线性代数和复杂的算术，都依赖于这样的结构属性。
The analysis of algorithms in IEEE floating-point arithmetic is most often carried out via repeated applications of the so-called standard model, which bounds the relative error of each basic operation by a common epsilon depending only on the format. While this approach has been eminently useful for establishing many accuracy and stability results, it fails to capture most of the low-level features that make floating-point arithmetic so highly structured. In this paper, we survey some of those properties and how to exploit them in rounding error analysis. In particular, we review some recent improvements of several classical, Wilkinson-style error bounds from linear algebra and complex arithmetic that all rely on such structure properties.