Optimal (N-1)-step fixed-point algorithms correspond exactly to (N-1)! arc diagrams that support composition, decomposition, and H-duality while producing new quasi-anytime optimal methods.
Mean value methods in iteration.Proceedings of the American Mathematical Society, 4(3): 506–510
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A Theory of Composition and Duality of Extremal Optimal Fixed-Point Algorithms
Optimal (N-1)-step fixed-point algorithms correspond exactly to (N-1)! arc diagrams that support composition, decomposition, and H-duality while producing new quasi-anytime optimal methods.