A proof of convergence and an error bound for the method of bisection in
Author:
Baker Kearfott
Journal:
Math. Comp. 32 (1978), 11471153
MSC:
Primary 65H10
MathSciNet review:
0494897
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: Let be an msimplex in . We define "bisection" of S as follows. We find the longest edge of S, calculate its midpoint , and define two new msimplexes 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 .
 [1]
P. ALEXANDROFF & H. HOPF, Topologie, Chelsea, New York, 1935; reprinted 1973.
 [2]
Marvin
J. Greenberg, Lectures on algebraic topology, W. A. Benjamin,
Inc., New YorkAmsterdam, 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]
Baker
Kearfott, An efficient degreecomputation method for a generalized
method of bisection, Numer. Math. 32 (1979),
no. 2, 109–127. MR 529902
(80g:65062), http://dx.doi.org/10.1007/BF01404868
 [5]
Ivo
G. Rosenberg and Frank
Stenger, A lower bound on the angles of
triangles constructed by bisecting the longest side, Math. Comp. 29 (1975), 390–395. MR 0375068
(51 #11264), http://dx.doi.org/10.1090/S00255718197503750685
 [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. 2328.
 [1]
 P. ALEXANDROFF & H. HOPF, Topologie, Chelsea, New York, 1935; reprinted 1973.
 [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 degreecomputation 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. 390395. 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. 2328.
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
65H10
Retrieve articles in all journals
with MSC:
65H10
Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197804948973
PII:
S 00255718(1978)04948973
Article copyright:
© Copyright 1978
American Mathematical Society
