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1. LAGRANGE
INTERPOLATION
METHOD
Name:Bhuvaneshwari
Name:Bhuvaneshwari
Roll no: 22EE10

2. CONTENT
▪ About Joseph-Louis Lagrange
▪ Define Lagrange interpolation
▪ Formula
▪ Prove
▪ Question
▪ Inverse interpolation
▪ Question
▪ Advantages & Disadvantage
▪ Conclusion

3. About Joseph-Louis
Lagrange
Joseph Louis Lagrange (1736 -1813) From `A Short
Account of the History of Mathematics' (4th edition, 1908)
by W. W. Rouse Ball. Joseph Louis Lagrange, the
greatest mathematician of the eighteenth century, was
born at Turin on January 25, 1736, and died at Paris on
April 10, 1813.

4. Lagrange interpolation
Lagrange polynomials are used for polynomial interpolation.
For a given set of distinct points xj and numbers yj.
Lagrange’s interpolation is also an Nth degree polynomial
approximation to f(x).

5. Formula
▪ Aaaaaaaaaaaaaaaaaa
▪ This is called Lagrange's interpolation formula and can
be used and unequal intervals.

10. ▪ Question: Find the value of y when x=9
given
X 5 7 11 13 17
Y 150 392 1452 2366 5202

11. Inverse Interpolation
▪ Inverse interpolation is defined as the process of
finding the value of the argument corresponding to a
given value of the function lying between two tabulated
functional values.

12. ▪ Question: Find x when f(x)=15
X 5 6 9 11
Y 12 13 14 16

13. (15-13)(15-14)(15-16) (5) +(6) + (15-12)(15-13)(15-16)
(15-12)(15-14)(15-16)(9) +
(12-13)(12-14)(12-16) (13-12)(13-14)(13-16) (14-12)(14-13)(14-16)
(15-12)(15-13)(15-14) (11)
(16-12)(16-13)(16-14)

14. Advantages
▪ The formula is simple and easy to remember.
▪ There is no need to construct the divided difference table.
▪ The application of the formula is not speedy.

15. Disadvantage
▪ There is always a chance to committing some error.
▪ The calculation provide no check whether the
functional values used the taken correctly or not.

16. Conclusion
▪ Lagrange has a better performance at the boundaries
which makes it more convenient for real time applications.