John Travis
Mississippi College
For the following, enter data for x values in the list xs and corresponding y-values in the list ys. Watch as the linear system is created and solved so that the resulting interpolating polynomial is created and graphed.
xs = (-1,0,1,2,4)
ys = (4,-1,0,3,-5)
n = len(xs)
pts = []
for k in range(n):
pts.append((xs[k],ys[k]))
show(pts)
A = zero_matrix(QQ,n,n+1)
for k in range(n):
u = xs[k]
for j in range(n):
A[k,j] = u^j
A[k,n]=ys[k]
D = A.echelon_form()
show(A)
show(D)
G = points(pts,color='red',size=20)
f = D[0][5]+D[1][5]*x+D[2][5]*x^2+D[3][5]*x^3+D[4][5]*x^4
pretty_print(html("$ f(x) = %s$"%str(latex(f))))
G += plot(f,(x,min(xs)-0.5,max(xs)+0.5))
show(G)
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# as an interactive cell
reset()
@ interact
def _(xs = input_box(default=(-1,0,1,2,4)), ys = input_box(default=(4,-1,0,3,-5))):
n = len(xs)
pts = []
for k in range(n):
pts.append((xs[k],ys[k]))
# show(pts)
A = zero_matrix(QQ,n,n+1)
for k in range(n):
u = xs[k]
for j in range(n):
A[k,j] = u^j
A[k,n]=ys[k]
D = A.echelon_form()
show(A)
# show(D)
G = points(pts,color='red',size=20)
f = 0
for k in range(n):
f += D[k][n]*x^k
pretty_print(html("$ f(x) = %s$"%str(latex(f))))
G += plot(f,(x,min(xs)-0.5,max(xs)+0.5))
show(G)
Click to the left again to hide and once more to show the dynamic interactive window |
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