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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On faster convergence of the bisection method for all triangles
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by Martin Stynes PDF
Math. Comp. 35 (1980), 1195-1201 Request permission


Let $\Delta ABC$ be a triangle with vertices A, B, and C. It is "bisected" as follows: choose a/the longest side (say AB) of $\Delta ABC$, let D be the midpoint of AB, then replace $\Delta ABC$ by two triangles $\Delta ADC$ and $\Delta DBC$. Let ${\Delta _{01}}$ be a given triangle. Bisect ${\Delta _{01}}$ into two triangles ${\Delta _{11}}$ and ${\Delta _{12}}$. Next bisect each ${\Delta _{1i}},\;i = 1,2$, forming four new triangles ${\Delta _{2i}},\;i = 1,2,3,4$. Continue thus, forming an infinite sequence ${T_j},\;j = 0,1,2, \ldots$, of sets of triangles, where ${T_j} = \left \{ {{\Delta _{ji}}:1 \leqslant i \leqslant {2^j}} \right \}$. Let ${m_j}$ denote the mesh of ${T_j}$. It is shown that there exists $N = N({\Delta _{01}})$ such that, for $j \geqslant N$, ${m_{2j}} \leqslant {(\sqrt 3 /2)^N}{(1/2)^{j - N}}{m_0}$, thus greatly improving the previous best known bound of ${m_{2j}} \leqslant {(\sqrt 3 /2)^j}{m_0}$. It is also shown that only a finite number of distinct shapes occur among the triangles produced, and that, as the method proceeds, ${\Delta _{01}}$ tends to become covered by triangles which are approximately equilateral in a certain sense.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Math. Comp. 35 (1980), 1195-1201
  • MSC: Primary 51N99; Secondary 65B99, 65N30
  • DOI:
  • MathSciNet review: 583497