BandPC: Learning Residual-Band Preconditioner Combinations for Flexible Conjugate Gradient Solvers
The conjugate gradient (CG) method is a classical iterative solver for sparse symmetric positive definite (SPD) linear systems, but its convergence strongly depends on the spectral properties of the system matrix. Preconditioning can improve these properties; however, designing preconditioners that generalize across diverse and irregular sparsity patterns remains challenging. We propose BandPC (Band Preconditioner Combinations, where "Band" denotes residual-norm bands), a data-driven framework that leverages graph neural networks (GNNs) to predict multi-stage preconditioning strategies for the flexible conjugate gradient (FCG) method. BandPC partitions the FCG iteration into three residua...
| Authors | D. M. Li, Shang-Tian Yang, Xin Qiu |
|---|---|
| Primary category | math.NA |
| Published | 29 September 2026 |
| Last updated at source | 29 September 2026 |
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