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pro vyhledávání: '"Mascarenhas, Walter F."'
Autor:
Mascarenhas, Walter F.
We consider the solution of nonlinear equations in one real variable, the problem usually called by root finding. Although this is an old problem, we believe that some aspects of its solution using interval arithmetic are not well understood, and we
Externí odkaz:
http://arxiv.org/abs/2110.07126
Autor:
Mascarenhas, Walter F.
From a theoretical point of view, finding the solution set of a system of inequalities in only two variables is easy. However, if we want to get rigorous bounds on this set with floating point arithmetic, in all possible cases, then things are not so
Externí odkaz:
http://arxiv.org/abs/2109.09523
Autor:
Mascarenhas, Walter F.
IIn computational geometry, the construction of essential primitives like convex hulls, Voronoi diagrams and Delaunay triangulations require the evaluation of the signs of determinants, which are sums of products. The same signs are needed for the ex
Externí odkaz:
http://arxiv.org/abs/2109.07838
Autor:
Mascarenhas, Walter F.
Two articles published by Information Science discuss the derivatives of interval functions, in the sense of Svetoslav Markov. The authors of these articles tried to characterize for which functions and points such derivatives exist. Unfortunately, t
Externí odkaz:
http://arxiv.org/abs/2109.04878
Autor:
Mascarenhas, Walter F.
We argue that reducing nonlinear programming problems to a simple canonical form is an effective way to analyze them, specially when the problem is degenerate and the usual linear independence hypothesis does not hold. To illustrate this fact we solv
Externí odkaz:
http://arxiv.org/abs/1803.11304
Autor:
Mascarenhas, Walter F.
This article presents the Moore library for interval arithmetic in C++20. It gives examples of how the library can be used, and explains the basic principles underlying its design.
Comment: arXiv admin note: text overlap with arXiv:1611.09567"
Comment: arXiv admin note: text overlap with arXiv:1611.09567"
Externí odkaz:
http://arxiv.org/abs/1802.08558
Autor:
Mascarenhas, Walter F.
We extend the work by Mastroianni and Szabados regarding the barycentric interpolant introduced by J.-P. Berrut in 1988, for equally spaced nodes. We prove fully their first conjecture and present a proof of a weaker version of their second conjectur
Externí odkaz:
http://arxiv.org/abs/1708.04235
Autor:
Mascarenhas, Walter F.
We present the library Moore, which implements Interval Arithmetic in modern C++. This library is based on a new feature in the C++ language called concepts, which reduces the problems caused by template meta programming, and leads to a new approach
Externí odkaz:
http://arxiv.org/abs/1611.09567
Autor:
Mascarenhas, Walter F.
We present fast and accurate ways to normalize two and three dimensional vectors and quaternions and compute their length. Our approach is an adaptation of ideas used in the linear algebra library LAPACK, and we believe that the computational geometr
Externí odkaz:
http://arxiv.org/abs/1606.06508
Autor:
Mascarenhas, Walter F.
Floating point arithmetic allows us to use a finite machine, the digital computer, to reach conclusions about models based on continuous mathematics. In this article we work in the other direction, that is, we present examples in which continuous mat
Externí odkaz:
http://arxiv.org/abs/1605.09202