An inertial parallel algorithm for a finite family of $ G $-nonexpansive mappings applied to signal recovery

<abstract><p>This study investigates the weak convergence of the sequences generated by the inertial technique combining the parallel monotone hybrid method for finding a common fixed point of a finite family of $ G $-nonexpansive mappings under suitable conditions in Hilbert spaces endowed with graphs. Some numerical examples are also presented, providing applications to signal recovery under situations without knowing the type of noises. Besides, numerical experiments of the proposed algorithms, defined by different types of blurred matrices and noises on the algorithm, are able to show the efficiency and the implementation for LASSO problem in signal recovery.</p></abstract>

Computer simulation of the difference between Lasso and Lars

In order to correct the error that Efron et al pointed out that the modified Lars is a fast algorithm for lasso problem, computer simulation is carried out with data. The simulation results show that when a variable is removed first and then entered in the lasso problem, the variables selected by lasso and Lars cannot be the same. At this time, no matter how to modify the size of the variables selected by Lars, the lasso problem cannot be solved. The computer simulation method is used to correct the errors of Efron et al in this paper, and contribute to development of world data computing.

Bounded Perturbation Resilience of Two Modified Relaxed CQ Algorithms for the Multiple-Sets Split Feasibility Problem

In this paper, we present some modified relaxed CQ algorithms with different kinds of step size and perturbation to solve the Multiple-sets Split Feasibility Problem (MSSFP). Under mild assumptions, we establish weak convergence and prove the bounded perturbation resilience of the proposed algorithms in Hilbert spaces. Treating appropriate inertial terms as bounded perturbations, we construct the inertial acceleration versions of the corresponding algorithms. Finally, for the LASSO problem and three experimental examples, numerical computations are given to demonstrate the efficiency of the proposed algorithms and the validity of the inertial perturbation.