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- Newton's method is not good if your starting value is too far from the root
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Classroom Contents
Inverses and Newton's Method in Computational Thinking - Lecture 5
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- 1 - Introduction/Announcements
- 2 - Non-linear maps continued
- 3 - Invite to interact on Discord
- 4 - Another example of perspective projection
- 5 - Definition of a linear transformation
- 6 - Linearity relation is simply matrix times vector
- 7 - What is a matrix multiplication?
- 8 - Visual representation of how it works
- 9 - Coordinate transformations vs object transformations
- 10 - Julia: Images are arrays
- 11 - Julia: Probing a pixel
- 12 - Linking image coordinates (i,j) to spatial coordinates (x,y)
- 13 - Transforming image of a Corgi
- 14 - Function to transform xy to ij
- 15 - Creating reusable functions
- 16 - Inverse functions
- 17 - Trying different scaling
- 18 - What does inverse really do?
- 19 - Inverting non-linear transformations
- 20 - Bringing it all together
- 21 - Collisions
- 22 - Why are we doing this backwards?
- 23 - David takes over for the next part - Motivation
- 24 - What does it mean by calculating an inverse?
- 25 - Newton's method in 1D
- 26 - How does it work? - Interactive visualization using Plots.jl
- 27 - Trying the same with a new function
- 28 - What happens if we start from a different initial value?
- 29 - Newton's method is not good if your starting value is too far from the root
- 30 - Julia: Using Symbolics.jl
- 31 - Julia: Using ForwardDiff
- 32 - Perturbation to a non-linear function
- 33 - Looking back at the interactive visualization for Newton's method
- 34 - Writing the mathematical expressions behind the visualization
- 35 - Expanding via the definition of a derivative
- 36 - Obtaining a generic expression for the solution
- 37 - Julia: Implementing Newton's method in 1D
- 38 - Julia: For loop, x -= a is the same as x = x - a
- 39 - Derivatives in 2D
- 40 - Newton's method in 2D
- 41 - Changing to non-linear transformation
- 42 - Julia: Implementing Newton's method in 2D
- 43 - Julia: Use of the "\" operator
- 44 - Concluding remarks
