Lectures on Finite Precision Computations

摘要: Foreword Iain S. Duff Preface General Presentation Notations. Part I. Computability in Finite Precision: Well-Posed Problems Approximations Convergence Exact Arithmetic Precision Gaussian Elimination Forward Error Analysis The Influence of Singularities Numerical Stability for Iterative and Approximate Methods Limit Arithmetically Robust Computed Logistic Bibliographical Comments. II. Measures Regular Problems: Choice Data Class Perturbations Norms: Scaling Conditioning Simple Roots Polynomials Factorizations a Complex Matrix Solving Linear Systems Functions Square Concluding Remarks III. Computation the Neighbourhood Singularity: Singular Which are Condition Numbers Holder-Singularities Ill-Posed z ----> A - zI Distances to Singularity Unfolding Spectral Portraits IV. Quality Reliable Algorithms: Backward Analyses Software Formulae Errors Refinement Reliability V. Solvers Stopping Criteria Revisited Care Use PartVI. Tools Round-Off Algorithms. Historical Perspective Assessment Libraries Sensitivity Interval Probabilisitc Models Computer Algebra VII. Toolbox PRECISE Experimentation. What is PRECISE? Module Sample Size with Dangerous Border Summary 1 VIII. Experiments PRECISE. Format Examples Distance Eigenvalue Conclusion IX. Robustness Nonnormality. Nonnormality Instability Physics Technology on Qualitative Computing. Pseudosolutions F (x) = y: Pseudospectra Matrices Pseudozeroes Divergence Portrait Iteration Jordan Form Beyond Perturbation Theory XI. More Illustrations PRECISE: Annex: MATLAB Index Bibliography.