A Comparison of Image and Scalar-Based Approaches in Preconditioner Selection

2023/12/25 by Michael Souza, Luiz Mariano Carvalho, Souza, Michael +9 · 1 citation
Computer Science · Engineering · #65F08 #65F10 #68T20 #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.2312.15747

openalex publication_date 2023/12/25 · openalex created_date 2023/12/29 · openalex updated_date 2026/07/28

Abstract

Within high-performance computing (HPC), solving large sparse linear systems efficiently remains paramount, with iterative methods being the predominant choice. However, the performance of these methods is tightly coupled to the aptness of the chosen preconditioner. The multifaceted nature of sparse matrices makes the universal prescription of preconditioners elusive. Notably, the key attribute of sparsity is not precisely captured by scalar metrics such as bandwidth or matrix dimensions. Advancing prior methodologies, this research introduces matrix sparsity depiction via RGB images. Utilizing a convolutional neural network (CNN), the task of preconditioner selection turns into a multi-class classification problem. Extensive tests on 126 SuiteSparse matrices emphasize the enhanced prowess of the CNN model, noting a 32% boost in accuracy and a 25% reduction in computational slowdown.

Cited by

• Relative-Absolute Fusion: Rethinking Feature Extraction in Image-Based Iterative Method Selection for Solving Sparse Linear Systems

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