Skip to main content
Log in

Deforming subdivisions

  • Published:
Mathematical Programming Submit manuscript

Abstract

Subdivisions are continuously deformed subject to three local conditions and shown to retain the global property of being a subdivision. Cell maps, which are introduced, enable elementary arguments.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • B. Curtis Eaves, “A course in triangulations for solving equations with deformations,”Lecture Notes in Economics and Mathematical Systems 234 (1984).

  • B. Curtis Eaves and M.N. Broadie, “A variable rate refining triangulations for PL homotopies,” Department of Operations Research, Stanford University (Stanford, CA, 1983), in progress.

    Google Scholar 

  • C.B. Garcia and W.I. Zangwill, “A flex simplicial algorithm,” in: W. Forster, ed.,Numerical Solutions of Highly Nonlinear Problems (North-Holland, Amsterdam, 1980).

    Google Scholar 

  • M. Kojima, “A modification of Todd's triangulation J3,”Mathematical Programming 15 (1978) 223–227.

    Google Scholar 

  • G. van der Laan and A.J.J. Talman, “A new subdivision for computing fixed points with a homotopy algorithm,”Mathematical Programming 19 (1980) 78–91.

    Google Scholar 

  • 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, Department of Industrial Engineering, University of Michigan (Ann Arbor, MI, 1972).

    Google Scholar 

  • R. Saigal and M.J. Todd, “Efficient acceleration techniques for fixed point algorithms,”SIAM Journal on Numerical Analysis 15 (1978) 997–1007.

    Google Scholar 

  • S. Shamir, “Fixed-point computational methods—some new high performance triangulations and algorithms,” Ph.D. Thesis, Engineering-Economic Systems, Stanford University (Stanford, CA, 1979).

    Google Scholar 

  • M.J. Todd, “Improving the convergence of fixed-point algorithms,” in: M.L. Balinski and R.W. Cottle, eds.,Mathematical Programming Study 7 (1978) pp. 151–169.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This research is supported in part by the National Science Foundation Grant DMS-8902662.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Eaves, B.C. Deforming subdivisions. Mathematical Programming 48, 359–367 (1990). https://doi.org/10.1007/BF01582263

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01582263

Key words

Navigation