Interval Arithmetic and Its Implementations (Topology optimization theory and applications toward wide fields of natural sciences)

Abstract

A calculation method that derives mathematically correct results through numerical calculation, considering all the possible errors such as rounding errors and truncation errors, is called verified numerical computation . Recently, as a wide range of research activities on the verified numerical computation for various problems have been promoted by research groups in Japan such as those in Kyushu University and Waseda University, the calculation method has been widely acknowledged. This article describes specific implementation methods and notes on them, regarding the calculation methods in the interval operations, which are both the basis and basic operations of verified numerical computation.