Interpolation

Pronunciation: /ɪnˌtɜr pəˈleɪ ʃən/ Explain

Interpolation is a process for approximating the value of a function that is difficult to find. For example, say you want to approximate the value of square root of 3.7.

StepCalculationsDescription
1Start with 1 and 4.Find numbers larger and smaller than 3.7 that have easy to calculate square roots.
2square root of 1 equals 1. The square root of 1 is 1.
3square root of 4 equals 2. The square root of 4 is 2.
4(3.7-1)/(4-1) = 2.3/3 = 0.9 What part of the way is 3.7 between 1 and 4?
5(2-1)*0.9 = 0.9 About how much more is the square root of 3.7 than the square root of 1.
61+0.9 = 1.9 Approximate the square root of 3.7. The actual value of the square root of 3.7 is about 1.9235.

References

  1. Rice, Herbert L.. The Theory and Practice of Interpolation. www.archive.org. http://www.archive.org/stream/theorypracticeof00rice#page/n5/mode/1up. Buy the book
  2. Fraser, Duncan C.. Newton's Interpolation Formulas. vol LI pp 77-106,211-232 Oct 1918 - Aug 1919. www.archive.org. Reprinted from the Journal of the Institute of Actuaries. C. & E. Latton. http://www.archive.org/stream/newtonsinterpola00frasrich#page/n1/mode/2up. Buy the book
  3. Steffenson, J. F.. Interpolation. 2nd edition. Reprint from 1950 edition. Dover Publications. March 17, 2006. Last Accessed 8/6/2018. Buy the book

Cite this article as:

McAdams, David E. Interpolation. 8/7/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/i/interpolation.html.

Image Credits

Revision History

8/6/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
2/18/2010: Added "References". (McAdams, David E.)
12/2/2008: Changed equations to images. (McAdams, David E.)
9/16/2008: Initial version. (McAdams, David E.)

All Math Words Encyclopedia is a service of Life is a Story Problem LLC.
Copyright © 2018 Life is a Story Problem LLC. All rights reserved.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License