Polynomial interpolation & spline interpolation with MATLAB

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Carmine Caiaro

6:49:30

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1 - Introduction

1 - Preview.mp4

00:58

2 - Overview.mp4

04:18

3 - Definition of a polynomial function.mp4

03:55

4 - The monomial basis.mp4

02:35

5 - Basics about polynomial functions.mp4

19:39

6 - Quiz.mp4

12:35

2 - Evaluation of a polynomial function

7 - Usual evaluation & Horners method.mp4

10:14

8 - Horners method Examples.mp4

04:39

9 - Horners method Code.mp4

08:05

10 - Polynomial decomposition factorization.mp4

05:14

11 - Decomposition with Horner method Proof.mp4

09:58

12 - Repeated application of Horners method.mp4

11:54

13 - Horners method for derivatives.mp4

09:31

14 - Horners method for derivatives Example.mp4

03:38

15 - Horners method for derivatives Code.mp4

06:42

3 - Polynomial interpolation

16 - Introduction to interpolation.mp4

06:55

17 - Polynomial interpolation.mp4

04:42

18 - Reasons for the usage of polynomials for interpolation.mp4

01:56

19 - Interpolation via monomial basis.mp4

04:27

20 - Interpolation via monomial basis Example 1.mp4

02:16

21 - Interpolation via monomial basis Example 2.mp4

02:12

22 - Interpolation via monomial basis Code.mp4

03:19

23 - Interpolation via monomial basis Advantagesdisadvantages.mp4

09:52

24 - Uniqueness of the interpolating polynomial function.mp4

04:16

25 - Lagrange interpolation.mp4

09:26

26 - Lagrange interpolation Example 1.mp4

07:03

27 - Lagrange interpolation Example 2.mp4

08:03

28 - Lagrange interpolation Code.mp4

06:20

29 - Lagrange interpolation Advantagesdisadvantages.mp4

04:24

30 - Newton interpolation.mp4

07:19

31 - Newton interpolation Example 1.mp4

02:45

32 - Newton interpolation Example 2.mp4

06:24

33 - Newton interpolation Code.mp4

09:16

34 - Horners method for a Newton polynomial.mp4

04:38

35 - Newton interpolation Advantagesdisadvantages.mp4

04:42

4 - Interpolation error for an interpolating polynomial

36 - Formula & estimate for the interpolation error.mp4

07:28

37 - Chebyshev points & Runges phenomenon.mp4

08:47

38 - Proof of the theorem for the interpolation error.mp4

19:42

39 - Exercise 1 Polynomial interpolation & interpolation error.mp4

08:56

40 - Exercise 2 Piecewise linear interpolation.mp4

11:31

5 - Spline interpolation

41 - Definition & Motivation.mp4

07:37

42 - Linear spline interpolation.mp4

02:58

43 - Exercise 3 Linear spline interpolation.mp4

02:32

44 - Linear spline interpolation Code.mp4

09:40

45 - Cubic spline interpolation.mp4

12:47

46 - Derivation of the formula for a natural cubic interpolating spline.mp4

12:52

47 - Exercise 4 Natural cubic spline interpolation.mp4

09:41

48 - Natural cubic spline Code.mp4

13:29

49 - Remarks.mp4

11:39

6 - Matlab

50 - Matlab Live Script Horners method & polynomial interpolation.mp4

33:38

50 - pol-interpolation.zip

51 - Matlab Live Script Spline interpolation.mp4

08:48

51 - splines-interpolation.zip

7 - Conclusion

52 - Conclusion.mp4

03:15

Description

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

What You'll Learn?

Fast evaluation of polynomial functions, including Horner's method and Horner's method for derivatives
Polynomial interpolation, including interpolation via monomial basis, Lagrange interpolation and Newton interpolation
Spline interpolation, including linear spline interpolation and cubic spline interpolation
How to implement all discussed algorithms in MATLAB
The math behind all algorithms
How to use MATLAB to present your results graphically

Who is this for?

Engineering students

Science students

Anyone who has interest in interpolation

What You Need to Know?

Calculus and linear algebra knowledge at a beginner level (polynomials, continuous functions, linearity of functions, derivatives of functions, systems of linear equations, polynomial long division, ...)

You should know the low level basics of MATLAB (Syntax, functions, scripts, etc.)

MATLAB (already installed on your PC)

More details

Description
Through the study of mathematics I have acquired the method to questionize any algorithm down to the smallest detail before I start with the implementation.Â On the one hand it is a great feeling to fully understand an algorithm (The Aha! moment).Â On the other hand one can avoid many errors whose cause lie in the misunderstanding of the algorithm in this way.
Thus it is a big part of this course to enlight the math behind the treated algorithms.Â Â
Nevertheless programming techniques behind algorithms are also very important and will be treated as accurate as the the math on which the algorithms are based on.
Here we will consider the code for any algorithm for an implementation in MATLAB.
MATLAB is a fundamental and enormously powerful programming language. This language is nearly unavoidable if one consider a career in engineering, science or related fields. That is why this course is based on MATLAB.
This course is for everyone who wants to learn about interpolation.
In this course you will learn about:
Horner's method
Horner's method for derivatives
Polynomial interpolation, including interpolation via monomial basis, Lagrange interpolation and Newton interpolation
The interpolation error (How can one minimize or estimate this error?Â How do we proof the formula for the error bound?)
Spline interpolation, including linear spline interpolation and natural cubic spline interpolation
Derivation of the formula for the linear and the natural cubic spline interpolation
The code behind all methodsÂ
The math on which these algorithms are based on
How to use MATLAB to visualize your own examples
With this course you will obtain also two Matlab LiveÂ Scripts with all implementations and all discussed examples.
Who this course is for:
Engineering students
Science students
Anyone who has interest in interpolation

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MATLAB

Carmine Caiaro

Instructor's Courses

Hello, my name is Carmine and I am 24 years old. Currently I am studying mathematics in Germany.My subsidiary subject is computer science. I found my passion in the combination of these subjects, in the numerical analysis where I want to share my understanding and my knowledge now with other people.

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