Heavy Ball Restarted CMRH Methods for Linear Systems

Teng, Zhongming; Wang, Xuansheng

doi:10.3390/mca23010010

Cited by 2 publications

(2 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Restarted Heavy Ball Algorithm [16] is a variation of the Heavy Ball Algorithm that incorporates a restart mechanism. The restart mechanism is used to prevent the algorithm from getting stuck in a local minimum and allows it to escape from the current minimum and search for a better one.…”

Section: Restarted Heavy Ball Methodsmentioning

confidence: 99%

Streamlining Square Root Matrix Function Computation with Restarted Heavy Ball Algorithm

Karaduman

2023

Journal of Engineering Technology and Applied Sciences

View full text Add to dashboard Cite

This research proposes a new efficient algorithm for calculating the square root function of the large-scale nonsingular sparse matrix by restarting the Heavy Ball Algorithm. The square root matrix function is critical in various applications, including signal processing, image processing, and machine learning. However, its computation is challenging due to existing methods' high computational complexity and numerical instability. The restarted Heavy Ball Algorithm provides a streamlined and efficient approach for computing the square root matrix function. The approach demonstrates its effectiveness through numerical experiments on various matrices, showing its superior performance compared to existing state-of-the-art methods. Numerical results show that the restarted Heavy Ball algorithm is feasible and effective for calculating the square root function.

show abstract

Section: Restarted Heavy Ball Methodsmentioning

confidence: 99%

Streamlining Square Root Matrix Function Computation with Restarted Heavy Ball Algorithm

Karaduman

2023

Journal of Engineering Technology and Applied Sciences

View full text Add to dashboard Cite

show abstract

“…Our work is framed into the category of augmented methods that is a class of acceleration techniques. Some augmented methods are presented in [2,16,17,23].…”

Section: Introductionmentioning

confidence: 99%

Adaptive GMRES(m) for the Electromagnetic Scattering Problem

Espínola

Cabral

Schaerer

2020

Tend. Mat. Apl. Comput.

View full text Add to dashboard Cite

In this article, an adaptive version of the restarted GMRES (GMRES(m)) is introduced for the resolution of the finite difference approximation of the Helmholtz equation. It has been observed that the choice of the restart parameter m strongly affects the convergence of standard GMRES(m). To overcome this problem, the GMRES(m) is formulated as a control problem in order to adaptively combine two strategies: a) the appropriate variation of the restarted parameter m, if a stagnation in the convergence is detected; and b) the augmentation of the search subspace using vectors obtained at previous cycles. The proposal is compared with similar iterative methods of the literature based on standard GMRES(m) with fixed parameters. Numerical results for selected matrices suggest that the switching adaptive proposal method could overcome the stagnation observed in standard methods, and even improve the performance in terms of computational time and memory requirements.

show abstract

Heavy Ball Restarted CMRH Methods for Linear Systems

Cited by 2 publications

References 25 publications

Streamlining Square Root Matrix Function Computation with Restarted Heavy Ball Algorithm

Streamlining Square Root Matrix Function Computation with Restarted Heavy Ball Algorithm

Adaptive GMRES(m) for the Electromagnetic Scattering Problem

Contact Info

Product

Resources

About