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This paper intends to solve the time-varying Yang-Baxter-like matrix equation (TVYBLME), which is frequently employed in the fields of scientific computing and engineering applications. Due to its critical and promising role, several methods have been constructed to generate a high-performing solution for the TVYBLME. However, given the fact that noise is ubiquitous and inevitable in actual systems. It is necessary to design a computational algorithm with strong robustness to solve the TVYBLME, which has rarely been mentioned previously. For this reason, to remedy shortcomings that the conventional computing methods have encountered in a noisy case, a modified Newton integration (MNI) neural algorithm is proposed and employed to solve the TVYBLME. In addition, the related theoretical analyses show that the proposed MNI neural algorithm has the noise-tolerance ability under various noisy cases. Finally, the feasibility and superiority of the proposed MNI neural algorithm to solve the TVYBLME are verified by simulation experiments. [ABSTRACT FROM AUTHOR]

Sparse triangular solve (SpTRSV) is an important kernel in many scientific computing applications. In traditional viewpoints, accelerating SpTRSV by parallelizing the solution process is a challenging task. Dependencies among the variables that exist in the solution process not only restrict the parallelism that can be achieved, but also introduce large synchronization overhead among the parallel tasks. Moreover, a time-consuming pre-processing phase is commonly required to identify calculations that can be parallelized. However, we have observed that a large number of dependencies among the variables can be eliminated if we only calculate partial values of the variables first and add them together to obtain the final values later. By using such a strategy, starting to solve a variable does not need to wait for all of its prerequisite variables having been solved. In consequence, parallelism of the SpTRSV can be increased significantly. In this paper, we transform above mentioned observations into a subtree-based parallel algorithm to accelerate SpTRSV. The proposed algorithm calculates partial values of the variable along with an implicit subtree traversal and utilizes hardware atomic operation to implement accumulation of the partial values. This not only introduces no pre-processing overhead, but also avoids any barrier synchronization among the parallel threads. We evaluate the proposed algorithm on 2135 matrices from SuiteSparse Matrix Collection based on a generic GPU platform. Experimental results demonstrate that our scheme outperforms the state-of-the-art GPU and CPU vendor libraries in 1949 and 1782 matrices, respectively. Compared with the latest synchronization-free method, our scheme outperforms in 1779 matrices. [ABSTRACT FROM AUTHOR]