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A homotopy method for locating all zeros of a system of polynomials

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Functional Differential Equations and Approximation of Fixed Points

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

Supported in part by the National Science Foundation under MCS 76-06739

Supported in part by the National Science Foundation under MCS 76-07247-A03 and by the US Army Research Office under ARO-DAAG-76-GO294.

Supported in part by NSF Grant MCS76-24432.

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References

  1. Abraham, R. and Robbin, J., Transversal Mappings and Flows, Benjamin, New York, 1967.

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  2. Chow, S.-N., Mallet-Paret, J. and Yorke, J.A., Finding zeros of maps: homotopy methods that are constructive with probability one, Math. Comp. 32 (1978), 887–899.

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  3. Drexler, F.J., A homotopy method for the calculation of all zero-dimensional polynomial ideals, Continuation Methods, 69–93, H. Wacker (ed.), Academic Press, New York, 1978.

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  4. Garcia, C.B. and Zangwill, W.I., Global continuation methods for finding all solutions to polynomial systems of equations in N unknowns, preprint.

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  5. Li, T.-Y. and Yorke, J.A., Finding all the roots of polynomials by homotopy method — numerical investigation, in preparation.

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  6. Nirenberg, L., Topics in Nonlinear Functional Analysis, Courant Institute, New York University, 1974.

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  7. Watson, L., A globally convergent algorithm for computing fixed points of C1 maps, preprint.

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  8. Watson, L., Wang, C.-Y. and Li, T.-Y., The elliptic porus slider — a homotopy method, J. Applied Mechanics, 45 (1978), 435–436.

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Authors
  1. Shui-Nee Chow
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  2. John Mallet-Paret
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  3. James A. Yorke
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Editor information

Heinz-Otto Peitgen Hans-Otto Walther

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© 1979 Springer-Verlag

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Chow, SN., Mallet-Paret, J., Yorke, J.A. (1979). A homotopy method for locating all zeros of a system of polynomials. 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/BFb0064312

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  • DOI: https://doi.org/10.1007/BFb0064312

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09518-7

  • Online ISBN: 978-3-540-35129-0

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