• ForewordPrefaceNotationChapter 1: General Presentation. CouplingChaotic ComputationsComputability in Finite PrecisionNumerical Quality of ComputationsRole of SingularitiesSpectral Instability and NonnormalityInfluence on Nonnumerical SoftwareQualitative ComputingExperimental MathematicsSense of Errors: For a Rehabilitation of Finite Precision ComputationsChapter 2: Computability in Finite PrecisionWell-Posed ProblemsApproximationsConvergence in Exact ArithmeticComputability in Finite PrecisionGaussian EliminationForward Error AnalysisThe Influence of SingularitiesNumerical Stability in Exact ArithmeticComputability in Finite Precision for Iterative and Approximate MethodsThe Limit of Numerical Stability in Finite PrecisionArithmetically Robust ConvergenceThe Computed LogisticBibliographical CommentsChapter 3: Measures of Stability for Regular ProblemsChoice of Data and Class of PerturbationsChoice of Norms: ScalingConditioning of Regular ProblemsSimple Roots of PolynomialsFactorizations of a Complex MatrixSolving Linear SystemsFunctions of a Square MatrixConcluding RemarksBibliographical Comments. Chapter 4: Computation in the Neighbourhood of a SingularitySingular Problems That Are Well PosedCondition Numbers of Hölder SingularitiesComputability of Ill-Posed ProblemsSingularities of z * A * zIDistances to SingularityUnfolding of SingularitySpectral PortraitsBibliographical CommentsChapter 5: Arithmetic Quality of Reliable AlgorithmsForward and Backward AnalysesBackward ErrorQuality of Reliable SoftwareFormulae for Backward ErrorsInfluence of the Class of PerturbationsIterative Refinement for Backward StabilityRobust Reliability and Arithmetic QualityBibliographical CommentsChapter 6: Numerical Stability in Finite PrecisionIterative and Approximate MethodsNumerical Convergence of Iterative SolversStopping Criteria in Finite PrecisionRobust ConvergenceThe Computed Logistic RevisitedCare of UseBibliographical CommentsChapter 7: Software Tools for Round-off Error Analysis in AlgorithmsA Historical PerspectiveAssessment of the Quality of Numerical SoftwareBackward Error Analysis in LibrariesSensitivity AnalysisInterval AnalysisProbabilistic ModelsComputer AlgebraBibliographical CommentsChapter 8: The Toolbox PRECISE for Computer ExperimentationWhat is PRECISE?Module for Backward Error AnalysisSample SizeBackward Analysis with PRECISEDangerous Border and Unfolding of a SingularitySummary of Module 1Bibliographical CommentsChapter 9: Experiments with PRECISE. Format of the ExamplesBackward Error Analysis for Linear SystemsComputer Unfolding of SingularityDangerous Border and Distance to SingularityRoots of PolynomialsEigenvalue ProblemsConclusionBibliographical CommentsChapter 10: Robustness to NonnormalityNonnormality and Spectral InstabilityNonnormality in Physics and TechnologyConvergence of Numerical Methods in Exact ArithmeticInfluence on Numerical SoftwareBibliographical CommentsChapter 11: Qualitative Computing. Sensitivity and Pseudosolutions for F (x) = yPseudospectra of MatricesPseudozeroes of PolynomialsDivergence Portrait for the Complex Logistic IterationQualitative Assessment of a Jordan FormBeyond Linear Perturbation TheoryBibliographical CommentsChapter 12: More Numerical Illustrations with PRECISEAnnex: The Toolbox PRECISE for MATLABBibliographyIndex.

'Chaitin-Chatelin and Fraysse provide a rigorous basis for error analysis and asses the quality and reliability of computations. ... Problems and algorithm derivations, toolboxes for computer experimentation, are given in a clear succinct form.' D. E. Bentil, CHOICE