Polynom-Interpolation Vandermonde-Lagrange-Newton
add nodes A, . . , D, E or delete nodes (max 9)
Input in AlgebraView or move nodes A, B, C, D in Graphics
XY={A, B, C, D, E}
polynom degree = count nodes - 1 (n=4)
(1) f_a:Take({a_0,a_1,a_2,a_3,a_4,a_5,a_6,a_7,a_8,a_9},1,n) →polynom coefficents
(2) f_X: Sequence(x^j , j, 0, n-1) → {1, x, x2, x3} polynom basis
(3) fo(x):=Sum(f_a f_X) → a3 x3+a2 x2+a1 x +a_0 general polynom function
(5) Sequence(fo(X(j)) = Y(j),j,1,n) →{fo(X(1)) = Y(1), fo(X(2)) = Y(2), fo(X(3)) = Y(3), fo(X(4)) = Y(4)}
(6) V:=Substitute(LeftSide($5), f_a=Identity(n)) → Vandermonde Matrix
App Kubisches Polynom (Vandermonde-Matrix) with annotations
Newton Polynom Coefficient Matrix (27) n=4
Newtonsches und Lagrangesches Interpolationsverfahren
App Kubisches Polynom (Vandermonde-Matrix) with annotations
Newton Polynom Coefficient Matrix (27) n=4
Newtonsches und Lagrangesches Interpolationsverfahren