Pedro Gonnet

Robust Padé approximation via SVD

Pade approximation is considered from the point of view of robust methods of numerical linear algebra, in particular, the singular value decomposition. This leads to an algorithm for practical computation that bypasses most problems of solution of nearly-singular systems and spurious pole-zero pairs caused by rounding errors, for which a MATLAB code is provided. The success of this algorithm suggests that there might be variants of Pade approximation that are pointwise convergent as the degrees of the numerator and denominator increase to

A review of error estimation in adaptive quadrature

\infty

Pairwise verlet lists: Combining cell lists and verlet lists to improve memory locality and parallelism

, unlike traditional Pade approximants, which converge only in measure or capacity.

Fast and Stable Rational Interpolation in Roots of Unity and Chebyshev points

The most critical component of any adaptive numerical quadrature routine is the estimation of the integration error. Since the publication of the first algorithms in the 1960s, many error estimation schemes have been presented, evaluated, and discussed. This article presents a review of existing error estimation techniques and discusses their differences and their common features. Some common shortcomings of these algorithms are discussed, and a new general error estimation technique is presented.

Stability of Barycentric Interpolation Formulas for Extrapolation

Verlet lists, which are commonly used in many particle‐based simulations, are not suited for modern, shared‐memory parallel multicore architectures. In this article, we introduce pairwise Verlet lists: local Verlet lists containing only interacting particle pairs between a pair of neighboring computational cells. We show that these pairwise Verlet lists are more efficient and scale much better than the traditional global Verlet list, both on a single processor as well as on multiple shared‐memory cores. The improved performance on a single core makes them an interesting option for distributed‐memory simulations as well.

A specialized ODE integrator for the efficient computation of parameter sensitivities.

A new method for interpolation by rational functions of prescribed numerator and denominator degrees is presented. When the interpolation nodes are roots of unity or Chebyshev points, the algorithm is particularly simple and relies on discrete Fourier transform matrices, which results in a fast implementation using the fast Fourier transform. The method is generalized for arbitrary grids, which requires the construction of polynomials orthogonal on the set of interpolation nodes. The appearance of common factors in the numerator and denominator due to finite-precision arithmetic is explained by the behavior of the singular values of the linear system associated with the rational interpolation problem. The new algorithm has connections with other methods, particularly the work of Jacobi and Kronecker, Berrut and Mittelmann, and Egecioglu and Koc. Short MATLAB codes and numerical experiments are included.

Efficient and Scalable Algorithms for Smoothed Particle Hydrodynamics on Hybrid Shared/Distributed-Memory Architectures

The barycentric interpolation formula defines a stable algorithm for evaluation at points in

Efficient Algorithms for Molecular Dynamics Simulations on the Cell Broadband Engine Architecture

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A short note on the fast evaluation of dihedral angle potentials and their derivatives

of polynomial interpolants through data on Chebyshev grids. Here it is shown that for evaluation at points in the complex plane outside

ROBUST RATIONAL INTERPOLATION AND LEAST-SQUARES ∗

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