Formal Proofs of Rounding Error Bounds

We prove the componentwise relative error bound 3u for the complex inversion algorithm (assuming p > 4), and we show that this bound is asymptotically optimal (as p → ∞) when p

This chapter is an introductory chapter: it recalls the definitions related to floating-point arithmetic, and presents some of the features of the IEEE-754-2008 Standard for

This analysis, however, does not suffice to improve the classical bounds (1.2) into the new ones in (1.1): for LU and Cholesky factorization and triangular system solving, what will

Cette étude a montré que les mesures issues des instruments AMSU quand elles sont combinées avec des estimations fiables de l’émissivité et de la température de surface,

Dans le scénario volontariste 2 (avec cogénération et récupération du CO 2 ), le volume du gaz naturel consommé pour la production d’électricité sera substitué par le

A lower density of keratinocytes does not allow proper reconstruction of the epidermis since, in this case, the culture medium can overlay the seeded

• We show that the recent probabilistic backward error analysis of Higham and Mary [ 16 ], which assumes that rounding errors are independent random variables with zero mean, holds

rounding error analysis, floating-point arithmetic, probabilistic error bounds, martingale, concentration inequality, mean independence, summation, inner product, matrix–vector