A new algebraic and arithmetic framework for interval computations
For researchers and practitioners using interval arithmetic, this work addresses fundamental algebraic limitations, though the abstract lacks concrete performance numbers.
The paper introduces a new algebraic framework for interval arithmetic that ensures distributivity, eliminating wrapping effects and data dependence. Applications include matrix eigenvalue calculations, symmetric matrix inversion, and optimization, demonstrated in Python.
In this paper we propose some very promissing results in interval arithmetics which permit to build well-defined arithmetics including distributivity of multiplication and division according addition and substraction. Thus, it allows to build all algebraic operations and functions on intervals. This will avoid completely the wrapping effects and data dependance. Some simple applications for matrix eigenvalues calculations, inversion of symmetric matrices and finally optimization are exhibited in the object-oriented programming language python.