Chaos in Relaxed Newton's Method: The Quadratic Case
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چکیده
In [8], Gilbert Strang explored the chaotic behavior of Newton's method applied to x + 1 when the iteration starts from only real initial conditions. We embed Strang's problem in the one-parameter family of iteration methods known as relaxed Newton's method. By extending this analysis to include a discussion of invariant measures, probability densities, and Lyapunov exponents, we prove that in the quadratic case, relaxed Newton's method exhibits chaotic dynamics as well.
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تاریخ انتشار 2002