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Complexity of the Bisection Method by Claudio Gutierrez; Flavio Gutierrez; Maria-Cecilia Rivara is a Computer Science article available to read on EtoBox.

What is Complexity of the Bisection Method about?

The bisection method is the consecutive bisection of a triangle by the median of the longest side. In this paper we prove a subexponential asymptotic upper bound for the number of similarity classes of triangles generated on a mesh obtained by iterative bisection, which previously was known only to be finite. The relevant parameter is γ /σ , where γ is the biggest and σ is the smallest angle of the triangle. We get this result by introducing a taxonomy of triangles that precisely captures the behaviour of the bisection method. We also prove that the number of directions on the plane given by the sides of the triangles generated is finite. Additionally, we give purely geometrical and intuitive proofs of classical results for the bisection method.

Who reads Complexity of the Bisection Method?

Author

Claudio Gutierrez; Flavio Gutierrez; Maria-Cecilia Rivara

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0304-3975)

Published

2007

Language

EN

Field

Computer Science (Physical Sciences)