other · Universidad de Chile · 2009

Complexity of the bisection method

Gutiérrez Gallardo, Claudio, Gutiérrez, Flavio, Rivara Zúñiga, María Cecilia

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Abstract

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

Cite this paper

APA 7

Gutiérrez Gallardo, C., Gutiérrez, F., & Rivara Zúñiga, M. C. (2009). Complexity of the bisection method. Universidad de Chile.

MLA 9

Gutiérrez Gallardo, Claudio, et al. “Complexity of the bisection method.” Universidad de Chile, 2009.

Chicago

Gutiérrez Gallardo, Claudio, Flavio Gutiérrez, and María Cecilia Rivara Zúñiga. 2009. “Complexity of the bisection method.” Universidad de Chile.

Harvard

Gutiérrez Gallardo, C., Gutiérrez, F. and Rivara Zúñiga, M.C. (2009) ‘Complexity of the bisection method’, Universidad de Chile.

BibTeX

@misc{gutierrezgallardo2009complexity,
  title = {{Complexity of the bisection method}},
  author = {Gutiérrez Gallardo, Claudio and Gutiérrez, Flavio and Rivara Zúñiga, María Cecilia},
  journal = {Universidad de Chile},
  year = {2009}
}

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