Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
ISSN-L : 2185-4106
Special Section on Verified Numerical Computations, Part I
The Essentials of verified numerical computations, rounding error analyses, interval arithmetic, and error-free transformations
Katsuhisa OzakiTakeshi Ogita
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2020 Volume 11 Issue 3 Pages 279-302

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Abstract

Floating-point numbers and floating-point arithmetic are widely used in numerical computations. A treatable problem size can quickly become large-scale due to the continual advancement of computational environments. If the number of floating-point operations increases, then problems caused by rounding errors become increasingly critical. In the worst case, an approximate solution obtained by a numerical computation can be inaccurate. Therefore, verified numerical computations are becoming increasingly important. This paper presents a survey of the basics related to verified numerical computations. We focus on floating-point arithmetic, interval arithmetic, rounding error analyses, and error-free transformations of floating-point operations.

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© 2020 The Institute of Electronics, Information and Communication Engineers
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