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AN ODD THEOREM.

Author: B C Eaves; STANFORD UNIV CA OPERATIONS RESEARCH HOUSE.
Publisher: Ft. Belvoir Defense Technical Information Center SEP 1969.
Edition/Format:   eBook : EnglishView all editions and formats
Database:WorldCat
Summary:
Let C be a bounded convex polyhedral set and let f:C(arrow)C be continuous and piecewise linear. Using notions from complementary pivot theory, it is shown that if each fixed point of f lies interior to some piece of linearity, then f has an odd number of fixed points. In addition, an algorithm is given for computing a fixed point of f.
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Material Type: Internet resource
Document Type: Internet Resource
All Authors / Contributors: B C Eaves; STANFORD UNIV CA OPERATIONS RESEARCH HOUSE.
OCLC Number: 227572299
Notes: Sponsored in part by Contracts DAHC04-67-C-0028, AT(04-3)-326 and by Grants NSF-GP-6431, PHS-GM-14789-02.
Description: 11 pages

Abstract:

Let C be a bounded convex polyhedral set and let f:C(arrow)C be continuous and piecewise linear. Using notions from complementary pivot theory, it is shown that if each fixed point of f lies interior to some piece of linearity, then f has an odd number of fixed points. In addition, an algorithm is given for computing a fixed point of f.

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