# Interpolation using four nodes

Suppose there are four points $(x_1,y_1),(x_2,y_2),(x_3,y_3),(x_4,y_4)$ my target is to interpolate any point $x_I$ between $x_2$ and $x_3$. Is there any Interpolation method which gives linear relation to find value of $y_I$ using above four point? I am looking for any numerical method or any approximation method (not Newton or Lagrange method)

• Yes I would try Lagrange – Ellya May 22 '14 at 6:29
• Would you accept a cubic polynomial ? If yes, I could elaborate. Could you show your points ? – Claude Leibovici May 22 '14 at 7:33
• @ClaudeLeibovici No, cubic polynomial is not required. – HelioVaGator May 22 '14 at 7:52
• @ClaudeLeibovici Actually i want to reduce multiplication part for reducing calculation time. If your method is faster or other than normal interpolating method (i.e n node point is given it can be approximately represented by a polynomial of n-1 degree), i will be glad to know. – HelioVaGator May 22 '14 at 8:04
• @ClaudeLeibovici sample points are (.81,.0117),(.90,.0186),(1.00,03058),(1.1,0.7861) – HelioVaGator May 22 '14 at 8:08