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Fixed Point Iterations Via Linear Mappings

open access: yesFixed Point Iterations Via Linear Mappings
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Jackknifing fixed points of iterations

Biometrika, 1987
The jackknife method for estimating the dispersion of a statistic T, considered as an estimator of a p-dimensional vector of parameters, can be modified so as to become computationally feasible for the class of statistics that are obtained as limits of iterative processes. Examples are given to show how the method can be applied to the EM algorithm and
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Iterative construction of fixed points

Numerical Functional Analysis and Optimization, 1996
Abstract, It is proved that an Ishikawa—type iteration scheme converges to the fixed point of a generalized contraction map in a convex metric space. The class of generalized contraction maps includes all quasi—contraction maps.
S.N. Mishra, A.K. Kalinde
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Random Relaxation of Fixed-Point Iteration

SIAM Journal on Scientific Computing, 1996
The author considers a stochastic fixed-point iteration where each coordinate is updated with a certain probability and otherwise left unchanged. The iteration is interesting from the viewpoint of parallel distributed computation because the realized sequences belong to the class of asynchronous fixed-point iterations.
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