Abstract
Motivated by operator splitting, a new two-stage-splitting iteration is proposed for the solution of maximum penalized likelihood estimation (MPLE) problems. The resulting algorithm, called two-step-late (TSL), is as practical and as easily implemented as the one-step-late (OSL) algorithm. Matrix analysis is applied to compare the rates of convergence of the TSL and OSL algorithms. It is proved that under quite general conditions for which OSL and TSL converge to the same solution the rate of convergence of TSL exceeds that of two steps of OSL, which is its computational counterpart. Numerical experimentation can then be used to check the range of the smoothing parameter for which these proofs hold.
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