On the bisection method for triangles

Adler, Andrew

doi:10.1090/S0025-5718-1983-0689473-5

On the bisection method for triangles
HTML articles powered by AMS MathViewer

by Andrew Adler PDF

Math. Comp. 40 (1983), 571-574 Request permission

Abstract:

Let UVW be a triangle with vertices U, V, and W. It is "bisected" as follows: choose a longest edge (say VW) of UVW, and let A be the midpoint of VW. The UVW gives birth to two daughter triangles UVA and UWA. Continue this bisection process forever. We prove that the infinite family of triangles so obtained falls into finitely many similarity classes, and we obtain sharp estimates for the longest jth generation edge.

References

Charles Harvey and Frank Stenger, A two-dimensional analogue to the method of bisections for solving nonlinear equations, Quart. Appl. Math. 33 (1975/76), no. 4, 351–368. MR 455361, DOI 10.1090/S0033-569X-1976-0455361-7
Baker Kearfott, A proof of convergence and an error bound for the method of bisection in $\textbf {R}^{n}$, Math. Comp. 32 (1978), no. 144, 1147–1153. MR 494897, DOI 10.1090/S0025-5718-1978-0494897-3
Krzysztof Sikorski, A three-dimensional analogue to the method of bisections for solving nonlinear equations, Math. Comp. 33 (1979), no. 146, 722–738. MR 521286, DOI 10.1090/S0025-5718-1979-0521286-6
Frank Stenger, Computing the topological degree of a mapping in $\textbf {R}^{n}$, Numer. Math. 25 (1975/76), no. 1, 23–38. MR 394639, DOI 10.1007/BF01419526
Martin Stynes, On faster convergence of the bisection method for certain triangles, Math. Comp. 33 (1979), no. 146, 717–721. MR 521285, DOI 10.1090/S0025-5718-1979-0521285-4