Abstract
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.
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© 1975 Springer-Verlag Berlin Heidelberg
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Moore, R.E. (1975). Two-sided approximation to solutions of nonlinear operator equations-a comparison of methods from classical analysis, functional analysis, and interval analysis. In: Nickel, K. (eds) Interval Mathematics. IMath 1975. Lecture Notes in Computer Science, vol 29. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07170-9_4
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DOI: https://doi.org/10.1007/3-540-07170-9_4
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