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Extension of Bolzano search to rectangles which preserves rectangles as iterates
Author(s) -
Troutt Marvin D.
Publication year - 1987
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(198708)34:4<593::aid-nav3220340411>3.0.co;2-h
Subject(s) - iterated function , extension (predicate logic) , mathematics , multivariable calculus , class (philosophy) , algorithm , computer science , artificial intelligence , programming language , mathematical analysis , control engineering , engineering
Abstract Multivariable elimination algorithms, which may be regarded as generalizations of various one‐dimensional search procedures, have not found wide application. A probable reason may be the generally very irregularly shaped regions of uncertainty that evolve iteratively in the procedures. Hence hope for practical salvage of this class of algorithms seems to lie in controlling the shape of the successively smaller regions of uncertainty. In this article an extension of Bolzano search to rectangles which preserves rectangular iterates is given. Since the result is essentially geometrical in nature, a geometric proof of this procedure is given. Hopefully the proof procedure will be of independent interest. A numerical illustration of the procedure is given for a game problem, such problems lending themselves to this method.