Improved block preconditioners for linear systems arising from half-quadratic image restoration

Wang, Chaojie; Li, Hongyi; Zhao, Debin

doi:10.1016/j.amc.2019.124614

Cited by 5 publications

(2 citation statements)

References 11 publications

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“…The performance of iterative methods for these problems is normally decided by the choice of preconditioning techniques. In recent years, a lot of preconditioning methods have been presented in various fields [4]- [9]. It has been attracted extensive attentions to propose preconditioning techniques for the structured linear equations appearing in the optimal control problem with different PDE constraints, boundary conditions and control types.…”

Section: Introductionmentioning

confidence: 99%

Beijing Language and Culture University, China

Wang¹

2022

The Experience of Examining the PhD

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In the study of network synchronization, an outstanding question of both theoretical and practical significance is how to allocate a given set of heterogenous oscillators on a complex network in order for improving the synchronization performance. Whereas methods have been proposed to address this question in literature, the methods are based on accurate models describing the system dynamics, which, however, are normally unavailable in realistic situations. Here we show that this question can be addressed by the model-free technique of feed-forward neural network (FNN) in machine learning. Specifically, we measure the synchronization performance of a number of allocation schemes and use the measured data to train a machine. It is found that the trained machine is able to not only infer the synchronization performance of any new allocation scheme, but also find from a huge amount of candidates the optimal allocation scheme for synchronization.

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Section: Introductionmentioning

confidence: 99%

Beijing Language and Culture University, China

Wang¹

2022

The Experience of Examining the PhD

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“…The efficient solution of the PDE-constrained optimization problem is of great importance in many areas of science and engineering. The performance of iterative methods for these problems depends highly on the choice of preconditioners, which are drawing more and more attention in various fields [1][2][3][4][5][6][7][8][9][10]. Extensive attention has been drawn to preconditioning the saddle point problem arising from the PDE-constrained optimization problem with different PDE constraints, boundary conditions and control types.…”

Section: Introductionmentioning

confidence: 99%

A Matching-Strategy-Inspired Preconditioning for Elliptic Optimal Control Problems

2023

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In this paper, a new preconditioning method is proposed for the linear system arising from the elliptic optimal control problem. It is based on row permutations of the linear system and approximations of the corresponding Schur complement inspired by the matching strategy. The eigenvalue bounds of the preconditioned matrices are shown to be independent of mesh size and regularization parameter. Numerical results illustrate the efficiency of the proposed preconditioning methods.

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