Interpolation

Pronunciation: /ɪnˌtɜr pəˈleɪ ʃən/ ?

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. interpolation. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=interpolation&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  2. Rice, Herbert L.. The Theory and Practice of Interpolation. (Accessed: 2010-02-18). http://www.archive.org/stream/theorypracticeof00rice#page/n5/mode/1up.
  3. Fraser, Duncan C.. Newton's Interpolation Formulas. Reprinted from the Journal of the Institute of Actuaries, vol LI pp 77-106,211-232 Oct 1918 - Aug 1919. C. & E. Latton. http://www.archive.org/stream/newtonsinterpola00frasrich#page/n1/mode/2up.
  4. Steffenson, J. F.. Interpolation, 2nd edition. Reprint from 1950 edition. Dover Publications, March 17, 2006. (Accessed: 2010-02-18).

Printed Resources

Cite this article as:


Interpolation. 2010-02-18. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/i/interpolation.html.

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2010-02-18: Added "References" (McAdams, David.)
2008-12-02: Changed equations to images (McAdams, David.)
2008-09-16: Initial version (McAdams, David.)

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