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Numerical solution of a generalized eigenvalue problem for even mappings

Part of the Lecture Notes in Mathematics book series (LNM,volume 730)

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References

  1. H. Scarf, The approximation of fixed points of a continuous mapping, SIAM J. Appl. Math. 15 (1967), 1328–1343.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. B. C. Eaves, An odd theorem, Proc. Amer. Math. Soc. 26 (1970), 509–513.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. H.W. Kuhn, Simplicial approximation of fixed points, Proc. Nat. Acad. Sci. 61 (1968), 1238–1242.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. B. C. Eaves, Homotopies for the computation of fixed points, Math. Programming 3 (1972), 1–22.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. B. C. Eaves and R. Saigal, Homotopies for the computation of fixed points on unbounded regions, Math. Programming 3 (1972), 225–237.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. R. T. Willmuth, The computation of fixed points, Ph.D. Thesis, Dept. Operation Research, Stanford University, 1973.

    Google Scholar 

  7. B. C. Eaves and H. Scarf, The solution of systems of piecewise linear equations, Math. of Oper. Res. 1 (1976), 1–27.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. R. B. Kellogg, T. Y. Li and J. A. Yorke, A method of continuation for calculating a Brouwer fixed point. Computing Fixed points with Applications, S. Karamadian, ed., (Meeting Proceedings: Clemson, June, 1974), Academic Press, New York, 1977, 133–147.

    Google Scholar 

  9. R. B. Kellogg, T. Y. Li, and J. A. Yorke, A constructive proof of the Brouwer Fixed Point Theorem and computational results, SIAM J. Num. Anal. 13 (1976), 473–483.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. M. Hirsch, A proof of nonretractability of a cell onto its boundary. Proc. Amer. Math. Soc. 14 (1963), 364–365.

    MathSciNet  MATH  Google Scholar 

  11. L. Watson, Finding fixed points of C2 maps by using homotopy methods, Computation and Applied Math., to appear.

    Google Scholar 

  12. S. N. Chow, J. Mallet-Paret and J. A. Yorke, Finding zeroes of maps: homotopy methods that are constructive with probability one, to appear in J. Math. Computation.

    Google Scholar 

  13. S. Smale, A convergent process of price adjustment and global Newton methods, J. Math. Econ. 3 (1976), 1–14.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. M. Hirsch and S. Smale, personal communication.

    Google Scholar 

  15. J. Alexander and J. A. Yorke, Homotopy continuation method: numerically implementable topological procedure, Transactions Amer. Math. Soc., to appear.

    Google Scholar 

  16. P. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. Functional Anal. 7 (1971), 487–513.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. J. L. Kaplan and J. A. Yorke, Nonassociative, real algebras and quadratic differential equations, to appear in J. Nonlinear Analysis.

    Google Scholar 

  18. R. Abraham and J. Robbin, Transversal mappings and flows, Benjamin, N.Y., 1967.

    MATH  Google Scholar 

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© 1979 Springer-Verlag

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Kaplan, J.L., Yorke, J.A. (1979). Numerical solution of a generalized eigenvalue problem for even mappings. 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/BFb0064320

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  • DOI: https://doi.org/10.1007/BFb0064320

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  • Print ISBN: 978-3-540-09518-7

  • Online ISBN: 978-3-540-35129-0

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