34 citations · 63 across the 16 of their papers we have counts for
19 papers
Root Finding With Interval Arithmetic
Walter F. Mascarenhas
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 i…
Solving systems of inequalities in two variables with floating point arithmetic
Walter F. Mascarenhas
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 fl…
Computing the exact sign of sums of products with floating point arithmetic
Walter F. Mascarenhas
IIn computational geometry, the construction of essential primitives like convex hulls, Voronoi diagrams and Delaunay triangulations require the evaluation of the signs of determin…
On the differentiability of interval functions
Walter F. Mascarenhas
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 f…
A simple canonical form for nonlinear programming problems and its use
Walter F. Mascarenhas
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…
Moore: Interval Arithmetic in C++20
Walter F. Mascarenhas
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.
On the rate of convergence of Berrut's interpolant at equally spaced nodes
Walter F. Mascarenhas
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 conjec…
Moore: Interval Arithmetic in Modern C++
Walter F. Mascarenhas
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 prob…
Fast and accurate normalization of vectors and quaternions
Walter F. Mascarenhas
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…
Floating point numbers are real numbers
Walter F. Mascarenhas
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…
A rational Rodrigues' formula to interpolate rotations
Walter F. Mascarenhas
We propose a rational version of the classic Rodrigues' rotation formula, which leads to a more accurate and efficient modelling of rotations and their derivatives in finite precis…
The stability of extended Floater-Hormann interpolants
Andre Pierro de Camargo, Walter F. Mascarenhas
We present a new analysis of the stability of extended Floater-Hormann interpolants, in which both noisy data and rounding errors are considered. Contrary to what is claimed in the…
On the backward stability of the second barycentric formula for interpolation
Walter F. Mascarenhas, Andre Pierro de Camargo
We present a new stability analysis for the second barycentric formula for interpolation, showing that this formula is backward stable when the relevant Lebesgue constant is small.
The divergence of the barycentric Pade approximants
Walter F. Mascarenhas
We explain that, like the usual Padé approximants, the barycentric Padé approximants proposed recently by Brezinski and Redivo-Zaglia can diverge. More precisely, we show that for…
The divergence of the BFGS and Gauss Newton Methods
Walter F. Mascarenhas
We present examples of divergence for the BFGS and Gauss Newton methods. These examples have objective functions with bounded level sets and other properties concerning the example…
The effects of rounding errors in the nodes on barycentric interpolation
Walter F. Mascarenhas, André Pierro de Camargo
We analyze the effects of rounding errors in the nodes on barycentric interpolation. These errors are particularly relevant for the first barycentric formula with the Chebyshev poi…
The stability of barycentric interpolation at the Chebyshev points of the second kind
Walter F. Mascarenhas
We present a new analysis of the stability of the first and second barycentric formulae for interpolation at the Chebyshev points of the second kind. Our theory shows that the seco…
Robust Pade approximants may have spurious poles
Walter F. Mascarenhas
We show that robust Pade approximants may have spurious poles and may not converge pointwise
Inference for eigenvalues and eigenvectors of Gaussian symmetric matrices
Armin Schwartzman, Walter F. Mascarenhas, Jonathan E. Taylor
This article presents maximum likelihood estimators (MLEs) and log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitr…