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  3. Interval Methods for Systems of Equations
  • Cited by 242
      • A. Neumaier, Albert-Ludwigs-Universität Freiburg, Germany
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    • Publisher:
      Cambridge University Press
      Publication date:
      September 2009
      January 1991
      ISBN:
      9780511526473
      9780521331968
      9780521102148
      DOI:
      https://doi.org/10.1017/CBO9780511526473
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.503kg, 272 Pages
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.39kg, 272 Pages
      • Subjects:
      Mathematics (general), Mathematics, Real and Complex Analysis, Numerical Analysis and Computational Science
      Series:
      Encyclopedia of Mathematics and its Applications (37)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Real and Complex Analysis, Numerical Analysis and Computational Science
    Series:
    Encyclopedia of Mathematics and its Applications (37)
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    Book description

    An interval is a natural way of specifying a number that is specified only within certain tolerances. Interval analysis consists of the tools and methods needed to solve linear and nonlinear systems of equations in the presence of data uncertainties. Applications include the sensitivity analysis of solutions of equations depending on parameters, the solution of global nonlinear problems, and the verification of results obtained by finite-precision arithmetic. In this book emphasis is laid on those aspects of the theory which are useful in actual computations. On the other hand, the theory is developed with full mathematical rigour. In order to keep the book self-contained, various results from linear algebra (Perron-Frobenius theory, M- and H- matrices) and analysis (existence of solutions to nonlinear systems) are proved, often from a novel and more general viewpoint. An extensive bibliography is included.

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