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Mathematical Preliminaries

In: C++ Toolbox for Verified Computing I

Author

Listed:
  • Ulrich Kulisch

    (Universität Karlsruhe, Institut für Angewandte Mathematik)

  • Rolf Hammer

    (Universität Karlsruhe, Institut für Angewandte Mathematik)

  • Matthias Hocks

    (Universität Karlsruhe, Institut für Angewandte Mathematik)

  • Dietmar Ratz

    (Universität Karlsruhe, Institut für Angewandte Mathematik)

Abstract

Interval arithmetic is the basic mathematical tool in verified numerical computing. This chapter summarizes the mathematical terms used in this book. After an introduction to real, complex, and extended interval arithmetic, we make some comments on the realization of arithmetics on a digital computer. We also touch on the problem of data conversion. Finally, we point out how to use fixed-point theorems to derive algorithms for verified numerical computing.

Suggested Citation

  • Ulrich Kulisch & Rolf Hammer & Matthias Hocks & Dietmar Ratz, 1995. "Mathematical Preliminaries," Springer Books, in: C++ Toolbox for Verified Computing I, chapter 0, pages 30-53, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-79651-7_3
    DOI: 10.1007/978-3-642-79651-7_3
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