Prove that the sun of the Lagrangian function is unity.
Answers
Answered by
0
Prove that the sum of the Lagrange (interpolation) coefficients is equal to 1.
Please suggest me a book-reference or give a solution for me. Thanks a lot in advance.
If f=∑ni=0f(xi)Li(x)f=∑i=0nf(xi)Li(x) then one has to prove∑ni=0Li(x)=1∑i=0nLi(x)=1 whereLi(x)=(x−x0)...(x−xi−1)(x−xi+1)...(x−xn)(xi−x0)...(xi−xi−1)(xi−xi+1)...(xi−xn)Li(x)=(x−x0)...(x−xi−1)(x−xi+1)...(x−xn)(xi−x0)...(xi−xi−1)(xi−xi+1)...(xi−xn),i=0⋯ni=0⋯n
share improve this question
askedJun 14 '15 at 18:39

user1942348
1,157●5●20
editedJun 14 '15 at 19:02
How do you define the Lagrange interpolation coefficients? – copper.hat Jun 14 '15 at 18:
Please suggest me a book-reference or give a solution for me. Thanks a lot in advance.
If f=∑ni=0f(xi)Li(x)f=∑i=0nf(xi)Li(x) then one has to prove∑ni=0Li(x)=1∑i=0nLi(x)=1 whereLi(x)=(x−x0)...(x−xi−1)(x−xi+1)...(x−xn)(xi−x0)...(xi−xi−1)(xi−xi+1)...(xi−xn)Li(x)=(x−x0)...(x−xi−1)(x−xi+1)...(x−xn)(xi−x0)...(xi−xi−1)(xi−xi+1)...(xi−xn),i=0⋯ni=0⋯n
share improve this question
askedJun 14 '15 at 18:39

user1942348
1,157●5●20
editedJun 14 '15 at 19:02
How do you define the Lagrange interpolation coefficients? – copper.hat Jun 14 '15 at 18:
Similar questions