IFSA/NAFIPS 2019 2019: Fuzzy Techniques: Theory and Applications pp 330-339

# A Neglected Theorem - Numerical Analysis via Variable Interval Computing

• Tsau Young Lin
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1000)

## Abstract

A neglected theorem in numerical computing is proved. In science labs, the computing of a scientific formula $$y_0 = E(x_0)$$ is often approximated by computing an ‘adequately close’ finite decimal f, namely, E(f). In essence, numerical computing is approximate computing: A finite decimal, say $$f = 0.333$$, can be rounded from any reals in [0.3325, 0.333), called rounding interval; so a computation of f is an approximate computing for any reals in this rounding interval. A real number, based on Cantor’s infinite decimal representation, can be regarded as a convergent sequence of rounding intervals. The computing of such sequences is variable interval computing – hope to be a useful approach to numerical analysis.

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