Details

Autor(en) / Beteiligte

• Adams, Ernst
• Kulisch, Ulrich

Titel

Scientific computing with automatic result verification

Beschreibungen/Notizen

• "The bulk of the papers collected in this book represent selected material taken from doctoral or diploma theses which were written at the Institute for Applied Mathematics at the University of Karlsruhe"--P. ix.
• Includes bibliographical references and index.
• Front Cover; Scientific Computing With Automatic Result Verification; Copyright Page; Contents; Contributors; Preface; Acknowledgements; Introduction; Part I. Language and Progmmmmg Support for Verified Scientific Computation; Chapter 1. PASCAL-XSC, New Concepts for Scientific Computation and Numerical Data Processing; Chapter 2. ACRITH-XSC, A Fortran-like Language for Verified Scientific Computing; Chapter 3. C-XSC, A Programming Environment for Verified Scientific Computing and Numerical Data Processing; Chapter 4. Proposal for Accurate Floating-Point Vector Arithmetic
• Part II. Enclosure Methods and Algorithms with Automatic Result VerificationChapter 5. Automatic Differentiation and Applications; Chapter 6. Numerical Quadrature by Extrapolation with Automatic Result Verification; Chapter 7. Numerical Integration in Two Dimensions with Automatic Result Verification; Chapter 8. Verified Solution of Integral Equations with Applications; Chapter 9. Enclosure Methods for Linear and Nonlinear Systems of Fredholm Integral Equations of the Second Kind
• Chapter 10. A Step Size Control for Lohner's Enclosure Algorithm for Ordinary Differential Equations with Initial ConditionsChapter 11. Interval Arithmetic in Staggered Correction Format; Part III. Applications in the Engineering Sciences; Chapter 12. Multiple Precision Computations with Result Verification; Chapter 13. Verification of Asymptotic Stability for Interval Matrices and Applications in Control Theory; Chapter 14. Numerical Reliability of MHD Flow Calculations; Chapter 15. The Reliability Question for Discretizations of Evolution Problems
• Part I: Theoretical Consideration on FailuresPart II: Practical Failures; Chapter 16. KKR Bandstructure Calculations, A Challenge to Numerical Accuracy; Chapter 17. A Hardware Kernel for Scientific/Engineering Computations; Chapter 18. Bibliography on Enclosure Methods and Related Topics; Index
• Scientific computing with automatic result verification
• English