Lagrangian Interpolation

[Albert Chan]

(03-14-2019 07:22 PM)PedroLeiva Wrote:  For 2nd order polynomials we can use your program, just loading three points;
so we cannot use it for 3rd. or 4th. order, considering we will need 4 or 5 points. Am I right?

Yes, you can!

It does not matter how many points. Example, for 5 points:

Code:

x1   y1
x2   y2  
x3   y3  y3'
x4   y4  y4'  
x5   y5  y5'  y5''

(x1,y1),(x2,y2),(x3,y3) --> (x3,y3')
(x1,y1),(x2,y2),(x4,y4) --> (x4,y4')
(x1,y1),(x2,y2),(x5,y5) --> (x5,y5')
(x3,y3'),(x4,y4'),(x5,y5') --> (x5,y5'')

This work with simple secant line too.

(03-07-2015 11:49 PM)bshoring Wrote:  A program for the HP-25 gave this example:

X1=-11 Y1=121 X2=3 Y2=9 X3=2 Y3=4
X=2.5 Y=6.25 etc.

Code:

    X   Y       Interpolate @ X=2.5
    2   4   
    3   9        6.5
  -11   121     -0.5    6.25

(2,4), (3,9) --> (2.5, 6.5)
(2,4), (-11,121) --> (2.5, -0.5)
(3,6.5), (-11,-0.5) --> (2.5, 6.25)