{"product_id":"lectures-on-finite-precision-computations-paperback-softback-9780898713589","title":"Lectures on Finite Precision Computations (Paperback \/ softback) 9780898713589","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eLectures on Finite Precision Computations\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThis book combines techniques from engineering and mathematics to describe the rigorous and novel theory of computability in finite precision.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eFrançoise Chaitin–chateli (Author), Valérie Frayssé (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780898713589\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 28 February 1997\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e252 pages\u003cbr\u003e22.8 x 15.1 x 1.4 cm, 0.455 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'Chaitin-Chatelin and Frayssé 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\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eDevoted to the assessment of the quality of numerical results produced by computers, this book addresses the question: How does finite precision affect the convergence of numerical methods on the computer when convergence has been proven in exact arithmetic? Finite precision computations are at the heart of the daily activities of many engineers and researchers in all branches of applied mathematics. Written in an informal style, the book combines techniques from engineering and mathematics to describe the rigorous and novel theory of computability in finite precision. In the challenging cases of nonlinear problems, theoretical analysis is supplemented by software tools to explore the stability on the computer. Roundoff errors are often considered negatively, as a severe limitation on the purity of exact computations. The authors show how the necessarily finite precision of the computer arithmetic can be turned into an asset to describe physical phenomena.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eForeword Iain S. Duff\u003cbr\u003e Preface\u003cbr\u003e General Presentation Notations. Part I. Computability in Finite Precision: Well-Posed Problems\u003cbr\u003e Approximations\u003cbr\u003e Convergence in Exact Arithmetic\u003cbr\u003e Computability in Finite Precision\u003cbr\u003e Gaussian Elimination\u003cbr\u003e Forward Error Analysis\u003cbr\u003e The Influence of Singularities\u003cbr\u003e Numerical Stability in Exact Arithmetic\u003cbr\u003e Computability in Finite Precision for Iterative and Approximate Methods\u003cbr\u003e The Limit of Numerical Stability in Finite Precision\u003cbr\u003e Arithmetically Robust Convergence\u003cbr\u003e The Computed Logistic\u003cbr\u003e Bibliographical Comments. Part II. Measures of Stability for Regular Problems: Choice of Data and Class of Perturbations\u003cbr\u003e Choice of Norms: Scaling\u003cbr\u003e Conditioning of Regular Problems\u003cbr\u003e Simple Roots of Polynomials\u003cbr\u003e Factorizations of a Complex Matrix\u003cbr\u003e Solving Linear Systems\u003cbr\u003e Functions of a Square Matrix\u003cbr\u003e Concluding Remarks\u003cbr\u003e Bibliographical Comments. Part III. Computation in the Neighbourhood of a Singularity: Singular Problems Which are Well-Posed\u003cbr\u003e Condition Numbers of Hölder-Singularities\u003cbr\u003e Computability of Ill-Posed Problems\u003cbr\u003e Singularities of z ----\u0026gt; A - zI\u003cbr\u003e Distances to Singularity\u003cbr\u003e Unfolding of Singularity\u003cbr\u003e Spectral Portraits\u003cbr\u003e Bibliographical Comments. Part IV. Arithmetic Quality of Reliable Algorithms: Forward and Backward Analyses\u003cbr\u003e Backward Error\u003cbr\u003e Quality of Reliable Software\u003cbr\u003e Formulae for Backward Errors\u003cbr\u003e Influence of the Class of Perturbations\u003cbr\u003e Iterative Refinement for Backward Stability\u003cbr\u003e Robust Reliability and Arithmetic Quality\u003cbr\u003e Bibliographical Comments. Part V. Numerical Stability in Finite Precision: Iterative and Approximate Methods\u003cbr\u003e Numerical Convergence of Iterative Solvers\u003cbr\u003e Stopping Criteria in Finite Precision\u003cbr\u003e Robust Convergence\u003cbr\u003e The Computed Logistic Revisited\u003cbr\u003e Care of Use\u003cbr\u003e Bibliographical Comments. PartVI. Software Tools for Round-Off Error Analysis in Algorithms. A Historical Perspective\u003cbr\u003e The Assessment of the Quality of the Numerical Software\u003cbr\u003e Backward Error Analysis in Libraries\u003cbr\u003e Sensitivity Analysis\u003cbr\u003e Interval Analysis\u003cbr\u003e Probabilisitc Models\u003cbr\u003e Computer Algebra\u003cbr\u003e Bibliographical Comments. Part VII. The Toolbox PRECISE for Computer Experimentation. What is PRECISE?\u003cbr\u003e Module for Backward Error Analysis\u003cbr\u003e Sample Size\u003cbr\u003e Backward Analysis with PRECISE\u003cbr\u003e Dangerous Border and Unfolding of a Singularity\u003cbr\u003e Summary of Module 1\u003cbr\u003e Bibliographical Comments. Part VIII. Experiments with PRECISE. Format of the Examples\u003cbr\u003e Backward Error Analysis for Linear Systems\u003cbr\u003e Computer Unfolding of Singularity\u003cbr\u003e Dangerous Border and Distance to Singularity\u003cbr\u003e Roots of Polynomials\u003cbr\u003e Eigenvalue Problems\u003cbr\u003e Conclusion\u003cbr\u003e Bibliographical Comments. Part IX. Robustness to Nonnormality. Nonnormality and Spectral Instability\u003cbr\u003e Nonnormality in Physics and Technology\u003cbr\u003e Convergence of Numerical Methods in Exact Arithmetic\u003cbr\u003e Influence on Numerical Software\u003cbr\u003e Bibliographical Comments. Part V. Qualitative Computing. Sensitivity and Pseudosolutions for F (x) = y: Pseudospectra of Matrices\u003cbr\u003e Pseudozeroes of Polynomials\u003cbr\u003e Divergence Portrait for the Complex Logistic Iteration\u003cbr\u003e Qualitative Computation of a Jordan Form\u003cbr\u003e Beyond Linear Perturbation Theory\u003cbr\u003e Bibliographical Comments. Part XI. More Numerical Illustrations with PRECISE: Annex: The Toolbox PRECISE for MATLAB\u003cbr\u003e Index\u003cbr\u003e Bibliography.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Miscellaneous items [\u003ca title=\"See our other books on Miscellaneous items\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Miscellaneous%20items%20%5BWZ%5D%22\"\u003eWZ\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"MP–SIA SIAM – Society for Industrial and Applied M","offers":[{"title":"Brand New","offer_id":52410746241304,"sku":"9780898713589","price":60.79,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9780898713589i.jpg?v=1784251361","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/lectures-on-finite-precision-computations-paperback-softback-9780898713589","provider":"Freshly Printed Books","version":"1.0","type":"link"}