Finite-order derivative information cannot accelerate worst-case fixed-point computation for smooth contractive mappings, proving Picard iteration is exactly optimal.
Oracle complexity of second-order methods for finite-sum problems.International Conference on Machine Learning, 2017
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Higher-Order Derivatives Do Not Accelerate the Computation of Fixed Points
Finite-order derivative information cannot accelerate worst-case fixed-point computation for smooth contractive mappings, proving Picard iteration is exactly optimal.