We introduce a methodology for obtaining inventories of error results for families of numerical dense linear algebra algorithms. The approach for deriving the analyses is goal-oriented, systematic, and layered. The presentation places the analysis side-by-side with the algorithm so that it is obvious where roundoff error is introduced. The approach supports the analysis of more complex algorith...

Shiu derives two formulas for calculating the probability of eventual ruin in a collective risk model. This paper implements one of the formulas by incorporating an algorithm to reduce round-off error due to convolution. It gives the results of the programs for some claim distributions. The usefulness of these two formulas is also discussed.

The CCSDS Telecommand (TC) and Telemetry (TM) standards are today being employed for a large number of scientific and commercial spacecraft. Using this standard allows reduced costs for on-board, ground and test equipment, as well as for spacecraft testing and in-orbit operation. This paper introduces the CCSDS/ESA standards, and presents the supporting standard components developed by ESA and ...

This paper deals with perturbed linear fixed point methods in the presence of round-off errors. Successive approximations as well as the more general asynchronous iterations are treated. Forward and backward error estimates are presented, and these are used to propose theoretical stopping criteria for these methods. In the case of asynchronous iterations, macro-iterations are used as a tool in ...

Rounding error may totally corrupt the result of a oating point computation.How to improve and validate the accuracy of a oating point computation, without largecomputing time overheads ? We contribute to this question considering two examples:polynomial evaluation and linear triangular system solving. In both cases we use thecompensation of the rounding errors to improve the ac...

The composite step biconjugate gradient method (CSBCG) is a simple modification of the standard biconjugate gradient algorithm (BCG) which smooths the sometimes erratic convergence of BCG by computing only a subset of the iterates. We show that 2 × 2 composite steps can cure breakdowns in the biconjugate gradient method caused by (near) singularity of principal submatrices of the tridiagonal ma...

It is of utmost interest to control the divergence of the magnetic flux in simulations of the ideal magnetohydrodynamic equations since, in general, divergence errors tend to accumulate and render the schemes unstable. This paper presents a higher-order extension of the locally divergence-preserving procedure developed in Torrilhon [M. Torrilhon, Locally divergence-preserving upwind finite volu...

Finite precision computations can severely affect the accuracy of computed solutions. We present a complete survey of a static analysis based on abstract interpretation, and a prototype implementing this analysis for C codes, for studying the propagation of rounding errors occurring at every intermediary step in floating-point computations. In the first part of this paper we briefly present all...

Both theory and implementations in deterministic global optimization have advanced significantly in the past decade. Two schools have developed: the first employs various bounding techniques without validation, while the second employs different techniques, in a way that always rigorously takes account of roundoff error (i.e. with validation). However, convex relaxations, until very recently us...

This paper describes an efficient and robust algorithm for computing a common refinement of two meshes modeling a common surface of arbitrary shape by overlaying them on top of each other. A common refinement is an important data structure for transferring data between meshes that have different topological structures. Our algorithm is optimal in time and space, with linear complexity. Special ...