Precise numerical computation

TL;DR: In this paper, a variable-step variable-order 3-stage Hermite-Birkhoff (HB) method is presented for solving non-stiff differential equations. But the method is not suitable for non-linear Vandermonde type systems.

TL;DR: A hardware-computed estimate of the roundoff error in floating-point computations is proposed, whose value is close to the relative error but does not have these anomalies and whose main cost issue might be the additional storage and the narrow datapath required for the estimate computation.

TL;DR: Results of accuracy analysis and error inspection imply that Gaussian dispersion models based on particle filtering and error propagation detection have better performance than traditional dispersion model in practice though sacrificing some computational efficiency.

TL;DR: In this paper, a demarche orientee modele is proposed for the development of a systeme de calcul based on the cooperation entre calcul formel et numerique, which is of type complementaire: les roles sont definis a priori.

TL;DR: This book gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic by combining algorithmic derivations, perturbation theory, and rounding error analysis.

TL;DR: The elementary theory of partitions and partitions in combinatorics can be found in this article, where the Hardy-Ramanujan-Rademacher expansion of p(n) is considered.

TL;DR: In this paper, the authors describe the basic properties of interval arithmetic and the solution of square linear systems of equations, and the Hull computation of nonlinear systems of equation 6, 7, 8.

TL;DR: Higham as discussed by the authors gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic, combining algorithmic derivations, perturbation theory, and rounding error analysis.