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An improvement of fixed point algorithms by using a good triangulation.(English)Zbl 0433.90089


MSC:

90C99 Mathematical programming
54H25 Fixed-point and coincidence theorems (topological aspects)
65K05 Numerical mathematical programming methods

Cite

References:

[1]B.C. Eaves, ”Homotopies for computation of fixed points”,Mathematical Programming 3 (1972) 1–22. ·Zbl 0276.55004 ·doi:10.1007/BF01584975
[2]B.C. Eaves and R. Saigal, ”Homotopies for computation of fixed points on unbounded regions”,Mathematical Programming 3 (1972) 225–237. ·Zbl 0258.65060 ·doi:10.1007/BF01584991
[3]R. Kellogg, T.Y. Li and J. Yorke, ”A constructive proof of Brouwer fixed point theorem and computation results”,SIAM Journal of Numerical Mathematics 13 (1976) 473–483. ·Zbl 0355.65037 ·doi:10.1137/0713041
[4]H.W. Kuhn, ”Some combinatorial lemmas in topology”,IBM Journal of Research and Development 4 (1960) 518–524. ·Zbl 0109.15603 ·doi:10.1147/rd.45.0518
[5]H.W. Kuhn and J.G. MacKinnon, ”Sandwich method for finding fixed points”,Journal of Optimization Theory and Applications 17 (1975) 189–204. ·Zbl 0299.65030 ·doi:10.1007/BF00933874
[6]G. van der Laan and A.J.J. Talman, ”A restart algorithm for computing fixed points without an extra dimension”,Mathematical Programming 17 (1979) 74–84. ·Zbl 0411.90061 ·doi:10.1007/BF01588226
[7]G. van der Laan and A.J.J. Talman, ”A restart algorithm without an artificial level for computing fixed points on unbounded regions” in: H.O. Peitgen and H.O. Walther, eds.,Functional differential equation and approximation of fixed points (Springer, Berlin, 1979). ·Zbl 0447.65019
[8]G. van der Laan and A.J.J. Talman, ”A new subdivision for computing fixed points with a homotopy algorithm”,Mathematical Programming, to appear. ·Zbl 0438.90104
[9]P.S. Mara, ”Triangulations of a cube”, M.S. Thesis, Colorado State University (Fort Collins, CO, 1972).
[10]O.H. Merrill, ”Applications and extensions of an algorithm that computes fixed points of certain upper semi-continuous point to set mappings”, Ph.D. Thesis, University of Michigan (Ann Arbor, MI, 1972).
[11]R. Saigal, ”Investigations into the efficiency of the fixed point algorithms”, in: S. Karamardian, ed.,Fixed points: algorithms and applications (Academic Press, New York, 1977) pp. 203–223.
[12]R. Saigal, D. Solow and L. Wolsey, ”A comparative study of two algorithms that compute fixed points in unbounded regions”, VIII International Symposium on Mathematical Programming (Stanford University, August 1973).
[13]H.E. Scarf, ”The approximation of fixed points of a continuous mapping”,SIAM Journal on Applied Mathematics 15 (1967) 1328–1343. ·Zbl 0153.49401 ·doi:10.1137/0115116
[14]H.E. Scarf (with the collaboration of T. Hansen),The computation of economic equilibria (Yale University Press, New Haven, CT, 1973).
[15]M.J. Todd, ”On triangulations for computing fixed points”,Mathematical Programming 10 (1976) 322–346. ·Zbl 0358.90047 ·doi:10.1007/BF01580679
[16]M.J. Todd, ”Improving the convergence of fixed point algorithms”,Mathematical Programming Study 7 (1978) 151–169. ·Zbl 0399.65034
[17]M.J. Todd, ”Fixed-point algorithms that allow restarting without an extra dimension”, Technical Report No. 379, Cornell University (Ithaca, NY, 1978).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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