Ch-5 computational method 2022 Interpolation and curve

Interpolation and curve

1. Outline: Introduction Curve fitting 2.1 Least –Square regression Linear regression Polynomial regression Multiple regression 2.2 Interpolation Newton’s Divided –Difference Interpolating polynomial Lagrange interpolating polynomial Cubic Spline Interpolation Computational Methods (EPCE 2204) Credit: 3 Hrs (Lecture: 2 Hr & Lab: 3 Hr ) __________________________________________ Chapter-Five Interpolation and Approximation Tamiru Getahun (MSc) ASTU

2. What is curve fitting and why we study it? Curve fitting refers to finding an appropriate mathematical model that expresses the relationship between a dependent variable Y and a single independent variable X and estimating the values of its parameters using Linear or nonlinear regression. Two types of curve fitting Least square regression Given data for discrete values, derive a single curve that represents the general trend of the data. When the given data exhibit a significant degree of error or noise. Interpolation Given data for discrete values, fit a curve or a series of curves that pass directly through each of the points. When data are very precise. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 2 Data are often given for discrete values along a continuum. However, you may require estimates at points between the discrete values. (x ,y ), (x 1 , y 1 ),………………….,( x n ,y n )

3. 5.1 Least Square Regression 1. Simple Linear Regression Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 3

4. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 4

5. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 5

6. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 6

7. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 7

8. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 8

9. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 9

10. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 10

11. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 11

12. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 12

13. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 13

14. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 14

15. 5.2 polynomial Interpolation Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 15

16. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 16

17. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 17

18. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 18

19. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 19

20. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 20

21. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 21

22. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 22

23. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 23

24. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 24

25. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 25

26. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 26

27. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 27

28. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 28

29. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 29

30. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 30

31. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 31

32. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 32

33. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 33

34. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 34

35. Interpolation and Approximation Tamiru G. G. (MSc) [email protected] ASTU – EPCE Dpt 35

36. Thank You For Your Attention! Questions?