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math.NA2023
About the ''accurate mode'' of the IEEE 1788-2015 standard for interval arithmetic
Nathalie Revol
The IEEE 1788-2015 standard for interval arithmetic defines three accuracy modes for the so-called set-based flavor: tightest, accurate and valid. This work in progress focuses on…
math.NA2022
Testing interval arithmetic libraries, including their IEEE-1788 compliance
Nathalie Revol, Luis Benet, Luca Ferranti +1
As developers of libraries implementing interval arithmetic, we faced the same difficulties when it came to testing our libraries. What must be tested? How can we devise relevant t…
math.NA2022
Affine Iterations and Wrapping Effect: Various Approaches
Nathalie Revol
Affine iterations of the form x(n+1) = Ax(n) + b converge, using real arithmetic, if the spectral radius of the matrix A is less than 1. However, substituting interval arithmetic t…