On the Limit of the Total Step Method in Interval Analysis

  • Günter Mayer
  • Ingo Warnke


We derive a linear system for the midpoint and the radius of the limit [xl* of the interval total step method [x]k+1 = [A][x]k +[b] provided that p(|[A]|) < 1. The coefficients of this system are formed by lower and upper bounds of the input intervals, their choice depends on the position of the components of [x](vn*) with respect to zero. For particular input data this choice can be made without knowing [x](vn*). For nonnegative [A] the coefficients are determined by solving at most n + 1 real linear systems.


Linear System Interval Arithmetic Unique Fixed Point Interval Vector Interval Matrix 
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Copyright information

© Springer-Verlag Wien 2001

Authors and Affiliations

  • Günter Mayer
    • 1
  • Ingo Warnke
    • 1
  1. 1.Fachbereich MathematikUniversität RostockRostockGermany

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