Contraction-Mapping | SpringerLink
Skip to main content

Contraction-Mapping

  • Reference work entry
Encyclopedia of Optimization
  • 586 Accesses

Article Outline

Keywords

Statement of the Result

Affine Problems

Nonlinear Problems

Integral Equations Example

See also

References

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

Access this chapter

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
JPY 3498
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
JPY 365365
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
JPY 397397
Price includes VAT (Japan)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Anselone PM (1971) Collectively compact operator approximation theory. Prentice-Hall, Englewood Cliffs, NJ

    MATH  Google Scholar 

  2. Atkinson KE (1973) Iterative variants of the Nyström method for the numerical solution of integral equations. Numer Math 22:17–31

    Article  MATH  MathSciNet  Google Scholar 

  3. Banach S (1922) Sur les opérations dans les ensembles abstraits et leur applications aux équations intégrales. Fundam Math 3:133–181

    MATH  Google Scholar 

  4. Brakhage H (1960) Über die numerische Behandlung von Integralgleichungen nach der Quadraturformelmethode. Numer Math 2:183–196

    Article  MATH  MathSciNet  Google Scholar 

  5. Briggs W (1987) A multigrid tutorial. SIAM, Philadelphia

    MATH  Google Scholar 

  6. Campbell SL, Ipsen ICF, Kelley CT, Meyer CD, Xue ZQ (1996) Convergence estimates for solution of integral equations with GMRES. J Integral Eq Appl 8:19–34

    Article  MATH  MathSciNet  Google Scholar 

  7. Dennis JE, Schnabel RB (1996) Numerical methods for nonlinear equations and unconstrained optimization. Classics Appl Math, vol 16, SIAM, Philadelphia

    MATH  Google Scholar 

  8. Golub GH, VanLoan CG (1983) Matrix computations. Johns Hopkins Univ. Press, Baltimore, MD

    MATH  Google Scholar 

  9. Hackbusch W (1985) Multi-grid methods and applications. Comput Math, vol 4. Springer, Berlin

    MATH  Google Scholar 

  10. Isaacson E, Keller HB (1966) Analysis of numerical methods. Wiley, New York

    MATH  Google Scholar 

  11. Kelley CT (1990) Operator prolongation methods for nonlinear equations. In: Allgower EL, Georg K (eds) Computational Solution of Nonlinear Systems of Equations. Lect Appl Math Amer Math Soc, Providence, RI, pp 359–388

    Google Scholar 

  12. Kelley CT (1995) A fast multilevel algorithm for integral equations. SIAM J Numer Anal 32:501–513

    Article  MATH  MathSciNet  Google Scholar 

  13. Kelley CT (1995) Iterative methods for linear and nonlinear equations. No. in Frontiers in Appl Math, vol 16 SIAM, Philadelphia

    MATH  Google Scholar 

  14. Ortega JM, Rheinboldt WC (1970) Iterative solution of nonlinear equations in several variables. Acad Press, New York

    MATH  Google Scholar 

  15. Saad Y, Schultz MH (1986) GMRES a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Statist Comput 7:856–869

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag

About this entry

Cite this entry

Kelley, C.T. (2008). Contraction-Mapping . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_92

Download citation

Publish with us

Policies and ethics