Newton's Iteration Method and its Generalizations

William J. Gilbert © 1991

Section 3: Newton Method

Section 3 text part 1 (10 Kbytes)
Figure 1: The Julia set of the Newton Method
for g(z) = (z - 1)(z + i)(z + 1 - i)		 Figure 2: Basins of attraction of the Newton Method
for g(z) = (z - 1)(z + i)(z + 1 - i)
Julia Set of Newtons Method (4 Kbytes) Newtons Method (5 Kbytes)

Section 3 text part 2 (3 Kbytes)
Figure 3a: Basins of attraction of the
Newton Method for
g(z) = (z - 1)(z + 0.5 - 0.33i)(z + 0.5 + 0.33i)		 Figure 3b: A magnification of Figure 3a
Bad Newtons Method (5 Kbytes) Bad Newtons Method Blowup (6 Kbytes)

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