As a new type of technique, simplicial methods have yielded
extremely important contributions toward solutions of a system of
nonlinear equations. Theoretical investigations and numerical tests
have shown that the performance of simplicial methods depends
critically on the triangulations underlying them. This monograph
describes some recent developments in triangulations and simplicial
methods. It includes the D1-triangulation and its applications to
simplicial methods. As a result, efficiency of simplicial methods
has been improved significantly. Thus more effective simplicial
methods have been developed.
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