Lagrange Interpolationspolynom pur
Author: Prof. Dr. Dörte Haftendorn
Date: Mai 06

Ha Mai 06

Interpolationspolynom, ziehe an den Punkten

Lagrange(x)=c0 la0(x)+c1 la1(x)+c2 la2(x)+c3 la3(x)

Linearkombination

A = (0.5385311372350271, 1.1269249056367214)
B = (0.9864207483934385, 2.3710627144100878)
D = (5, 1.5)
c0 = -0.015 (slider from -5 to 5, step 0.005)
C = (3.1263377794836273, 2.07246964030448)
c1 = -0.325 (slider from -5 to 5, step 0.005)
la1(x) = (((x - x(A)) * (x - x(C))) * (x - x(D)))
c3 = 0.075 (slider from -5 to 5, step 0.005)
la0(x) = (((x - x(B)) * (x - x(C))) * (x - x(D)))
la3(x) = (((x - x(A)) * (x - x(B))) * (x - x(C)))
la(x) = (((y(A) / ((((x(A) - x(B)) * (x(A) - x(C))) * (x(A) - x(D)))) * (x - x(B))) * (x - x(C))) * (x - x(D))) + (((y(B) / ((((x(B) - x(A)) * (x(B) - x(C))) * (x(B) - x(D)))) * (x - x(A))) * (x - x(C))) * (x - x(D))) + (((y(C) / ((((x(C) - x(A)) * (x(C) - x(B))) * (x(C) - x(D)))) * (x - x(A))) * (x - x(B))) * (x - x(D))) + (((y(D) / ((((x(D) - x(A)) * (x(D) - x(B))) * (x(D) - x(C)))) * (x - x(A))) * (x - x(B))) * (x - x(C)))
la0c(x) = (c0 * la0(x))
la1c(x) = (c1 * la1(x))
la2(x) = (((x - x(A)) * (x - x(B))) * (x - x(D)))
la3c(x) = (c3 * la3(x))
c2 = -0.37 (slider from -5 to 5, step 0.005)
la2c(x) = (c2 * la2(x))
Ax: (x(A), 0)
Bx: (x(B), 0)
Cx: (x(C), 0)
Dx: (x(D), 0)
f = Segment(A, Ax)
g = Segment(B, Bx)
h = Segment(C, Cx)
i = Segment(D, Dx)
Lagrange(x) = (c0 * la0(x)) + (c1 * la1(x)) + (c2 * la2(x)) + (c3 * la3(x))
p = Polynomial({A, B, C, D})