Improved error bounds for inner products in floating-point arithmetic

On the maximum relative error when computing integer powers by iterated multiplications in floating-point arithmetic..

Section II describes the 2-steps approach of the radix conversion, section III contains the algorithm for the exponent computation, section IV presents a novel approach of raising 5

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 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

• A posteriori error estimation tools used to compute the error • The computation of the bound is deterministic. • The second moment of the quantity of interest can be bounded –

Spruill, in a number of papers (see [12], [13], [14] and [15]) proposed a technique for the (interpolation and extrapolation) estimation of a function and its derivatives, when

Lately, there is an increasing interest on the use of goal-oriented error estimates which help to measure and control the local error on a linear or

A posteriori implicit residual-type estimators have traditionally been the most commonly used tech- niques to provide bounds of the error of the finite element method,