Newton-Raphson method visualized

This is a demonstration of oscillatory behavior of Newton-Raphson method. The example was borrowed from Wiki and modified a little bit.

Initial setup

First of all, create a line that lies on the x-axis. We will be taking the intersection of tangent to the curve and x-axis repeatedly, and this line will come in handy.

• a
• b
• define x-axis
• define color
• set line color

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Now, define the polynomial

• pol
• define a color and set the color of the plot

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First iteration

• Start with an initial estimate of the root
• Evaluate the polynomial at
• Draw a line joining the input and output points,
• line from input to output

This is where we start to apply the method. We calculate the tangent at the point (x0,y0) and get the point i1 where it intersects with the x-axis.

• tangent0
• Set color of the tangent
• i1

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The x-coordinate of this intersection point is the next (hopefully better) approximation of the root. Let's do a few more iterations:

Iteration 2

• x1
• y1
• p1x
• p1y
• hide unnecessary points and lines
• line from input to output
• tangent1
• Change color of the tangent line
• i2

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Iteration 3

• x2
• y2
• p2x
• p2y
• hide unnecessary points and lines
• line from input to output
• tangent2
• Change color of the tangent line
• i3

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Iteration 4

• x3
• y3
• p3x
• p3y
• hide unnecessary points and lines
• line from input to output
• tangent3
• Change color of the tangent line
• i4

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Iteration 5

• x4
• y4
• p4x
• p4y
• hide unnecessary points and lines
• line from input to output
• tangent4
• Change color of the tangent line
• i5
• x5