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Interpolation, Regression, and Smoothing

  • Erdogan Madenci
  • Atila Barut
  • Mehmet Dorduncu
Chapter

Abstract

Interpolation and regression of data and smoothing of noisy data play a significant role in many scientific disciplines. Interpolation is an estimation of an unknown variable at output points (locations) by employing the known values at surrounding input points. Regression is an estimation of a variable at both input and output points by employing the known values at the surrounding input locations. Smoothing is an estimation of a variable at only known input points by employing the known input values. Smoothing may be necessary if the input data is noisy. It is worth noting that interpolation is different than regression and smoothing; the estimation based on interpolation passes through all the known input values. In other words, there is an exact recovery of the known values of the input points. There exist several methods for such estimations.

References

  1. Liszka T (1984) An interpolation method for an irregular net of nodes. International Journal for Numerical Methods in Engineering 20: 1599–1612CrossRefGoogle Scholar
  2. Liszka T, Orkisz J (1980) The Finite Difference Method at Arbitrary Irregular Grids and Its Application in Applied Mechanics. Computers and Structures 11: 83–95.MathSciNetCrossRefGoogle Scholar
  3. Liu CS, Atluri S.N (2009), A fictitious time integration method for the numerical solution of the Fredholm integral equation and for numerical differentiation of noisy data, and its relation to the filter theory, CMES: Computer Modeling in Engineering 41:243–261.MathSciNetzbMATHGoogle Scholar
  4. Madenci E, Barut A, Futch M (2016) Peridynamic differential operator and its applications. Comput Methods in Appl Mech Eng 304:408–451MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Erdogan Madenci
    • 1
  • Atila Barut
    • 1
  • Mehmet Dorduncu
    • 1
  1. 1.Aerospace and Mechanical Engineering DepartmentUniversity of ArizonaTucsonUSA

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