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ALLGOWER, E., and M. JEPPSON, The Approximation of Solution of Nonlinear Elliptic Boundary Value Problems Having Several Solutions, to appear soon in Springer Lecture Notes, Ed: R. Ansorge and W. Törnig, Numerische, Insbesondere Approximationstheoretische Behandlung von Funktionslgleichungen, 1973.
ALLGOWER, E., and M. JEPPSON, Numerical Solution of Nonlinear Boundary Value Problems with Several Solutions, to appear soon.
COHEN, D.I.A., On the Sperner Lemma, J. Comb. Theory 2 (1967), 585–587.
COTTLE, R.W., Complementarity and Variational Problems, TR SOL 74–6, May 1974, Department of Operations Research, Stanford University.
EAVES, B.C., Homotopies for Computation of Fixed Points, Mathematical Programming 3, 1 (1972) 1–22.
EAVES, B.C., A Short Course in Solving Equations with PL Homotopies, SIAM-AMS Proceedings, Vol. IX (1976) 73–143.
EAVES, B.C. and R. SAIGAL, Homotopies for Computation of Fixed Points, Mathematical Programming 3, 2 (1972), 225–237.
EAVES, B.C. and H. SCARF, The Solution of Systems of Piecewise Linear Equations, Mathematics of Operations Research 1, 1 (1976), 1–27.
FREIDENFELDS, J., A Set of Intersection Theorem and Applications, Mathematical Programming 7, 2 (1974), 199–211.
GARCIA, C. B. and F.J. GOULD, An Improved Scalar Generated Homotopy Path for Solving f(x)=0, Center for Mathematical Studies in Business and Economics, Report #7633, University of Chicago, September 1976.
GARCIA, B.C., A Fixed Point Theorem Including the Last Theorem of Poincaré, Mathematical Programming 8, 2 (1975), 227–239.
HIRSCH, M.W., A Proof of the Nonretractability of a Cell onto its Boundary, Prodeedings of AMS, 14 (1963), 364–365.
HIRSCH, M.W., and S. SMALE, On Algorithms for Solving f(x)=0, Department of Mathematics, University of California, Berkeley.
KANEKO, I., A Mathematical Programming Method for the Inelastic Analysis of Reinforced Concrete Frames, TR 76–2 (1976), Department of Industrial Engineering, University of Wisconsin.
KATZENELSON, J., An Algorithm for Solving Nonlinear Resistor Networks, Bell Telephone Technical Journal, 44 (1965), 1605–1620.
KELLOGG, R.B., T.Y. LI, and J. YORKE, A Constructive Proof of the Brouwer Fixed Point Theorem and Computational Results, unpublished paper, University of Maryland and University of Utah (1975).
KOJIMA, M., On the Homotopic Approach to Systems of Equations with Separable Map**s, B-26, Department of Information Sciences, Tokyo Institute of Technology (1975).
KUHN, H.W., A New Proof of the Fundamental Theorem of Algebra, Mathematical Programming, Study 1(1974), 148–158.
LEMKE, C.E., Bimatrix Equilibrium Points and Mathematical Programming, Management Sciences, 11 (1965), 681–689.
LEMKE, C.E. and J.T. HOWSON, Jr., Equilibrium Points of Bimatrix Games, SIAM Journal on Applied Mathematics 12, 2 (1964), 413–423.
LI, T-Y, Path Following Approaches for Solving Nonlinear Equations: Homotopy, Continuous Newton and Projection, Department of Mathematics, Michigan State University, East Lansing, Michigan.
MERRILL, O.H., Applications and Extensions of an Algorithm that Computes Fixed Points of Certain Upper Semi-Continuous Point to Set Map**s, Ph.D. Dissertation, Department of Industrial Engineering, University of Michigan (1972)
MEYERSON, M.D., and O.H. WRIGHT, A New and Constructive Proof of the Borsak-Ulam Theorem, to appear in the Proceedings of the A.M.S.
NETRAVALI, A.N. and R. SAIGAL, Optimum Quantizer Design Using a Fixed-Point Algorithm, The Bell Telephone Technical Journal 55, 9 (1976), 1423–1435.
SAIGAL, R., On the Convergence Rate of Algorithms for Solving Equations that are Based on Complementarity Pivoting, Bell Telephone Laboratories, Holmdel, N.J.
SCARF, H., The Approximation of Fixed Points of a Continuous Map**, SIAM Journal on Applied Mathematics 15 5 (1967).
SCARF, H., The Core of an N Person Game, Econometrica 35, 1 (1967), 50–69.
SCARF, H., On the Computation of Equilibrium Prices, in Ten Economic Studies in the Tradition of Irving Fisher, John Wiley, New York (1967).
SCARF, H., and T. HANSEN, Computation of Economic Equilibria, Yale University Press, New Haven (1973).
SHAPLEY, L.S., On Balanced Games Without Side Payments, Mathematical Programming, Ed: T.C. Hu and S.M. Robinson, Academic Press, New York-London (1973), 261–290.
TODD, M.J., The Computation of Fixed Points and Applications, Springer-Verlag, Berlin-Heidelberg, 1976.
TODD, M.J., Exploiting Structure in Fixed Point Computation, Discussion Paper, Mathematics Research Center, University of Wisconsin, Madison, Wisconsin.
VAN DER LANN, G., and A.J.J. TALMAN, A New Algorithm for Computing Fixed Points, Free University, Amsterdam (March 1978).
WILMUTH, R.J., The Computations of Fixed Points, Ph.D. Thesis (1973), Department of Operations Research, Stanford University.
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Eaves, B.C. (1979). A view of complementary pivot theory (or solving equations with homotopies). In: Peitgen, HO., Walther, HO. (eds) Functional Differential Equations and Approximation of Fixed Points. Lecture Notes in Mathematics, vol 730. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064313
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DOI: https://doi.org/10.1007/BFb0064313
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