Simplex Bisection and Sperner Simplices

Από το τεύχος 44 του περιοδικού Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

The aim of the present paper is to describe an efficient numerical method for locating and computing solutions of systems of nonlinear algebraic and transcendental equations as well as the relationship between this method and the Sperner lemma. In particular, the author following the idea of using bisection based methods in problems concerning numerical simulations gives a generalized bisection method applied on n-dimensional simplexes by avoiding constructed Sperner simplices even though the structure of method is based on the existence of a Sperner simplex. Furthermore, it is proved that the above method converges rapidly to a solution of large and imprecise problems since the only computable information required is the algebraic signs of the components of the function. (This paper is based on a talk presented by the author in the 4th Panellenic Conference on Geometry on ``Research in Geometry and in its Teaching towards the 21st century'' taking place in the University of Patras, Greece, 28--30 May 1999.)

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