关键词: 带状矩阵, LU分解, 并行计算, 融合内核, 性能优化

Abstract: Band matrices are a class of sparse matrices characterized by non-zero elements concentrated around the main diagonal,and they are widely used in scientific computing and engineering simulations.LU factorization of such matrices plays a vital role in solving large-scale linear systems,particularly in simulation workloads,physical modeling,and engineering optimization problems.However,traditional LU factorization algorithms often suffer from limited parallelism and inefficient memory access patterns,which restrict their performance on modern hardware platforms.To address these challenges,this paper proposes a high-efficiency implementation and optimization strategy for band matrix LU decomposition on domestic domain-specific computing units(DCUs).The proposed method introduces two key techniques:one is a right-looking structure combined with a block partitioning strategy to improve computational locality and parallel execution efficiency;and the other is a high-performance panel factorization algorithm that reduces kernel launch frequency and global memory access overhead.Experimental results across different matrix sizes and bandwidths demonstrate that the proposed GPU-based implementation consistently outperforms CPU-based LAPACK and Intel MKL solutions in terms of runtime and resource utilization,while preserving numerical stability.Empirical results show that this approach exhibits strong scalability and practical engineering value,providing theoretical foundations and practical gui-dance for the efficient implementation of banded-matrix methods on heterogeneous parallel computing platforms.

Key words: Banded matrices, LU factorization, Parallel computing, Fusion kernel, Performance optimization