On the bisection method for triangles

Author:
Andrew Adler

Journal:
Math. Comp. **40** (1983), 571-574

MSC:
Primary 51M15; Secondary 51M20, 65L50, 65N50

DOI:
https://doi.org/10.1090/S0025-5718-1983-0689473-5

MathSciNet review:
689473

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Abstract | References | Similar Articles | Additional Information

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 *j*th generation edge.

**[1]**C. Harvey & F. Stenger, "A two dimensional analogue to the lethod of bisections for solving nonlinear equations."*Quart. Appl. Math.*, v. 33, 1976, pp. 351-368. MR**0455361 (56:13600)****[2]**R. B. Kearfott, "A proof of convergence and an error bound for the method of bisection in ,"*Math. Comp.*, v. 32, 1978, pp. 1147-1153. MR**0494897 (58:13677)****[3]**K. Sikorski, "A three-dimensional analogue to the method of bisections for solving nonlinear equations,"*Math. Comp.*, v. 33, 1979, pp. 722-738. MR**521286 (80i:65058)****[4]**F. Stenger, "Computing the topological degree of a mapping in*n*-space,"*Numer. Math.*, v. 25, 1975, pp. 23-38. MR**0394639 (52:15440)****[5]**M. Stynes, "On faster convergence of the bisection method for certain triangles,"*Math. Comp.*, v. 33, 1979, pp. 717-721. MR**521285 (80c:51020)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1983-0689473-5

Article copyright:
© Copyright 1983
American Mathematical Society