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With the help of the derivative of a mapping, the concept of the condition number can be extended to general mathematical tasks. Floating-point numbers define technically feasible subsets of real numbers. Their special arrangement guarantees that the relative rounding error is uniformly controlled by the so-called machine accuracy. Various stability concepts for numerical methods are associated with the condition number of the underlying mathematical task.

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General Condition Number and Floating Point Numbers

  • 章节

  • 发表日期：

    2025年

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  • Sören Bartels

摘要

With the help of the derivative of a mapping, the concept of the condition number can be extended to general mathematical tasks. Floating-point numbers define technically feasible subsets of real numbers. Their special arrangement guarantees that the relative rounding error is uniformly controlled by the so-called machine accuracy. Various stability concepts for numerical methods are associated with the condition number of the underlying mathematical task.