We propose a continuous approach for computing the pseudospectra of linear operators following a 'solve-then-discretize' strategy. Instead of taking a finite section approach or using a finite-dimensional matrix to approximate the operator of interest, the new method employs an operator analogue of the Lanczos process to work directly with operators and functions. The method is shown to be free of spectral pollution and spectral invisibility, fully adaptive, nearly optimal in accuracy, and well-conditioned. The advantages of the method are demonstrated by extensive numerical examples and comparison with the traditional method.

翻译：我们提出了一种遵循“先求解再离散化”策略的连续方法，用于计算线性算子的伪谱。新方法未采用有限截面逼近或使用有限维矩阵近似目标算子，而是利用算子的Lanczos过程类比直接作用于算子和函数。理论证明该方法无谱污染与谱不可见性、完全自适应、精度接近最优且条件数良好。通过大量数值算例及与传统方法的对比，本文展示了该方法的优越性。