Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to mitigate the computational burden associated with high-fidelity systems. We provide general error estimates under non-simple eigenvalue conditions, establishing the theoretical foundations for our methodology. Numerical examples, ranging from one-dimensional to three-dimensional setups, are presented to demonstrate the efficacy of reduced basis method in handling parametric variations in boundary conditions and coefficient fields to achieve significant computational savings while maintaining high accuracy, making them promising tools for practical applications in large-scale eigenvalue computations.

翻译：大规模特征值问题广泛出现于科学与工程的各个领域，对计算效率提出了极高要求。本研究针对参数化线性特征值问题的子空间逼近方法展开探讨，旨在减轻高保真系统带来的计算负担。我们在非单特征值条件下给出了一般性误差估计，为该方法奠定了理论基础。通过一维至三维的数值算例，我们展示了降基方法在处理边界条件与系数场的参数变化时的有效性，该方法在保持高精度的同时实现了显著的计算量节约，使其成为大规模特征值计算中极具应用前景的工具。