On the bisection method for triangles

Author:
Andrew Adler

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

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

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]**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**0455361****[2]**Baker Kearfott,*A proof of convergence and an error bound for the method of bisection in 𝑅ⁿ*, Math. Comp.**32**(1978), no. 144, 1147–1153. MR**0494897**, 10.1090/S0025-5718-1978-0494897-3**[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**, 10.1090/S0025-5718-1979-0521286-6**[4]**Frank Stenger,*Computing the topological degree of a mapping in 𝑅ⁿ*, Numer. Math.**25**(1975/76), no. 1, 23–38. MR**0394639****[5]**Martin Stynes,*On faster convergence of the bisection method for certain triangles*, Math. Comp.**33**(1979), no. 146, 717–721. MR**521285**, 10.1090/S0025-5718-1979-0521285-4

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Additional Information

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

Article copyright:
© Copyright 1983
American Mathematical Society