The contents of this brief Lecture Note are devoted to modeling, simulations, and applications
with the aim of proposing a unified multiscale approach accounting for the physics and the …

… In [48] the run-time complexity of symbolic/abstract simulation with Affine Arithmetic is
analyzed. It is shown that memory complexity is k + 2, and an overhead in run-time compared with …

Computing enclosures of the range of functions using interval arithmetic often leads to
overestimations due to variables (parameters) appearing more than once within the expression to …

… On the other hand, using our affine-arithmeticbased type we compute an absolute error
of 1.34 ∗ 10−15, which is (by the correctness of our approach) sound, yet several orders of …

… We use Affine Arithmetic (AA) for modeling the rounding errors of floating-point computations.
The derived rounding error bound by the AA-based error model is then used to determine …

This paper describes TANOR, an automated framework for designing hardware accelerators
for numerical computation on reconfigurable platforms. Applications utilizing numerical …

This text provides an introduction to the applications and implementations of partial differential
equations. The content is structured in three progressive levels which are suited for upper…

… One of these extensions is the so-called affine arithmetic [16], which incorporates the
signed amplitude of all the noise sources in the descriptions of all elements. Affine arithmetic …

… We will illustrate how interval and affine arithmetic compare to our tight polynomial bounds
when computing a two-dimensional axis-aligned bounding box of this curve over the domain, …

… the bounds computed in this way are very accurate and have no over-conservativeness,
which are suffered by some existing approaches such as interval arithmetic or affine arithmetic …