Polynomial interpolation & spline interpolation with MATLAB

سرفصل های دوره

Understand the math and the code behind the most common interpolation methods

1 - Introduction

1 - Preview

2 - Overview

3 - Definition of a polynomial function

4 - The monomial basis

5 - Basics about polynomial functions

6 - Quiz

2 - Evaluation of a polynomial function

7 - Usual evaluation & Horners method

8 - Horners method Examples

9 - Horners method Code

10 - Polynomial decomposition factorization

11 - Decomposition with Horner method Proof

12 - Repeated application of Horners method

13 - Horners method for derivatives

14 - Horners method for derivatives Example

15 - Horners method for derivatives Code

3 - Polynomial interpolation

16 - Introduction to interpolation

17 - Polynomial interpolation

18 - Reasons for the usage of polynomials for interpolation

19 - Interpolation via monomial basis

20 - Interpolation via monomial basis Example 1

21 - Interpolation via monomial basis Example 2

22 - Interpolation via monomial basis Code

23 - Interpolation via monomial basis Advantagesdisadvantages

24 - Uniqueness of the interpolating polynomial function

25 - Lagrange interpolation

26 - Lagrange interpolation Example 1

27 - Lagrange interpolation Example 2

28 - Lagrange interpolation Code

29 - Lagrange interpolation Advantagesdisadvantages

30 - Newton interpolation

31 - Newton interpolation Example 1

32 - Newton interpolation Example 2

33 - Newton interpolation Code

34 - Horners method for a Newton polynomial

35 - Newton interpolation Advantagesdisadvantages

4 - Interpolation error for an interpolating polynomial

36 - Formula & estimate for the interpolation error

37 - Chebyshev points & Runges phenomenon

38 - Proof of the theorem for the interpolation error

39 - Exercise 1 Polynomial interpolation & interpolation error

40 - Exercise 2 Piecewise linear interpolation

5 - Spline interpolation

41 - Definition & Motivation

42 - Linear spline interpolation

43 - Exercise 3 Linear spline interpolation

44 - Linear spline interpolation Code

45 - Cubic spline interpolation

46 - Derivation of the formula for a natural cubic interpolating spline

47 - Exercise 4 Natural cubic spline interpolation

48 - Natural cubic spline Code

49 - Remarks

6 - Matlab

50 - Matlab Live Script Horners method & polynomial interpolation

50 - pol-interpolation.zip

51 - Matlab Live Script Spline interpolation

51 - splines-interpolation.zip

7 - Conclusion

52 - Conclusion

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تولید کننده: Udemy-Training