Two-sided approximation to solutions of nonlinear operator equations-a comparison of methods from classical analysis, functional analysis, and interval analysis

  • R. E. Moore
Part of the Lecture Notes in Computer Science book series (LNCS, volume 29)


Two-sided approximation methods from classical and functional analysis require various conditions; ergo: monotonicity, Lipschitz, differentiability, or convexity. On the other hand, there are methods from interval analysis which require weaker conditions and which facilitate the construction of a suitable starting point for iterative computation. Specific methods from each of the three disciplines are given. An interval analytic method is shown to converge pointwise, inclusion-monotonically to an interval valued function. Illustrations are given in which the resulting function is sometimes the unique real solution of a given operator equation and sometimes an interval valued function containing a whole continuum of distinct real solutions. Thus, two-sided approximations can be computed for a whole family of solutions corresponding to initial or boundary data and constants known only to lie in certain intervals.


Interval Function Interval Analysis Interval Method Continuous Interval Interval Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • R. E. Moore
    • 1
  1. 1.University of WisconsinMadisonUSA

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