lagrange interpolation

computer oriented numerical technique

1. LAGRANGE INTERPOLATION METHOD

2. Presented by: group- 4 Akash Roushann 04 Ayush Raj 15 Md. Imran Alam 27 Sejal 40 Sumit 56 Komal Kumari 59

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

4. 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.

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

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

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

8. 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.

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

10. (15-13)(15-14)(15-16) (5 ) + (15-12)(15-14)(15-16) (6) + (15-12)(15-13)(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)

11. 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.

12. 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.

13. C onclusion Lagrange has a better performance at the boundaries which makes it more convenient for real time applications.

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