Sparse Matrix-Vector Multiplication (SpMV) is an essential sparse operation in scientific computing and artificial intelligence. Efficiently adapting SpMV algorithms to diverse matrices and architectures requires a framework capable of accurately recognizing sparse patterns and selecting the optimal implementation. In this work, we introduce Sparsity-aware SpMV (SSpMV), a framework that integrates expert-designed features with multimodal representations to adaptively predict the best-performing algorithm and parameters. For this purpose, we design a multimodal neural network called MM-Adapter, to capture diverse modalities to represent the computational features of SpMV. Experimental results demonstrate that MMAdapter achieves the highest accuracy of $81.05 \%$, outperforming existing SpMV prediction models. Furthermore, SSpMV consistently delivers substantial performance improvements over state-of-the-art sparse libraries across various multi-core platforms.

Multifrontal QR algorithm, which consists of symbolic analysis and numerical factorization, is a high-performance algorithm for orthogonal factorizing sparse matrix. In this work, a graph convolutional network (GCN) for adaptively selecting the optimal reordering algorithm is proposed in symbolic analysis. Using our GCN adaptive classifier, the average numerical factorization time is reduced by 20.78% compared with the default approach, and the additional memory overhead is approximately 4% higher than that of prior work. Moreover, for numerical factorization, an optimized tasks stream parallel processing strategy is proposed and a more efficient computing task mapping framework for NUMA architecture is adopted in this paper, which called STM-Multifrontal QR factorization. Numerical experiments on the TaiShan Server show average 1.22x performance gains over the original SuiteSparseQR. Nearly 80% of datasets have achieved better performance compared with the MKL sparse QR on Intel Xeon 6248.