Some algorithms that are known to converge can be renormalized at each iteration so that their local behavior can be seen. This creates dynamical systems that can be studied with modern tools, such as ergodic theory, chaos, special attractors, and Lyapounov exponents. This all feeds back to suggest new algorithms with faster rates of convergence. This unique work opens doors to new areas of investigation for researchers in dynamical systems, optimization, statistics, and computer science.
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Some algorithms that are known to converge can be renormalized at each iteration so that their local behavior can be seen. This creates dynamical systems that can be studied with modern tools, such as ergodic theory, chaos, special attractors, and Lyapounov exponents. This all feeds back to suggest new algorithms with faster rates of convergence. This unique work opens doors to new areas of investigation for researchers in dynamical systems, optimization, statistics, and computer science.
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