A proof of convergence and an error bound for the method of bisection in
Author:
Baker Kearfott
Journal:
Math. Comp. 32 (1978), 1147-1153
MSC:
Primary 65H10
DOI:
https://doi.org/10.1090/S0025-5718-1978-0494897-3
MathSciNet review:
0494897
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be an m-simplex in
. We define "bisection" of S as follows. We find the longest edge
of S, calculate its midpoint
, and define two new m-simplexes
and
by replacing
by M or
by M.
Suppose we bisect and
, and continue the process for p iterations. It is shown that the diameters of the resulting Simplexes are no greater then
times the diameter of the original simplex, where
is the largest integer less than or equal to
.
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- [2] MARVIN GREENBERG, Lectures on Algebraic Topology, Benjamin, New York, 1967. MR 0215295 (35:6137)
- [3] R. B. KEARFOTT, Computing the Degree of Maps and a Generalized Method of Bisection, Ph. D. dissertation, Univ. of Utah, 1977.
- [4] R. B. KEARFOTT, "An efficient degree-computation method for a generalized method of bisection," Numer. Math. (To appear.) MR 529902 (80g:65062)
- [5] J. ROSENBERG & F. STENGER, "A lower bound on the angles of triangles constructed by bisecting the longest side," Math. Comp., v. 29, 1975, pp. 390-395. MR 0375068 (51:11264)
- [6] MARTIN STYNES, An Algorithm for the Numerical Calculation of the Degree of a Mapping, Ph. D. dissertation, Oregon State Univ., 1977.
- [7]
FRANK STENGER, "An algorithm for the topological degree of a mapping in
," Numer. Math., v. 25, 1976, pp. 23-28.
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Additional Information
DOI:
https://doi.org/10.1090/S0025-5718-1978-0494897-3
Article copyright:
© Copyright 1978
American Mathematical Society