We present an advanced restrictively preconditioned biconjugate gradient-stabilized (RPBiCGSTAB) algorithm specifically designed to improve the convergence speed of Krylov subspace methods for nonlinear systems characterized by a structured 5-by-5 block configuration. This configuration frequently arises from cell-centered finite difference discretizations employed in solving image deblurring problems governed by mean curvature dynamics. The RPBiCGSTAB method is crafted to exploit this block structure, thereby optimizing both computational efficiency and convergence behavior in complex image processing tasks. Analyzing the spectral characteristics of preconditioned matrices often reveals a beneficial distribution of eigenvalues, which plays a critical role in accelerating the convergence of the RPBiCGSTAB algorithm. Furthermore, our numerical experiments validate the computational efficiency and practical applicability of the method in addressing nonlinear systems commonly encountered in image deblurring. Our analysis also extends to the spectral properties of the preconditioned matrices, noting a pronounced clustering of eigenvalues around 1, which contributes to enhanced stability and convergence performance.Through numerical simulations that focus on mean curvature-driven image deblurring, we highlight the superior performance of the RPBiCGSTAB method in comparison to other techniques in this specialized field.
Khalid et al. (Thu,) studied this question.
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