SIAM Review, Volume 63, Issue 3, Page 489-524, January 2021.
Using the resolvent operator, we develop an algorithm for computing smoothed approximations of spectral measures associated with self-adjoint operators. The algorithm can achieve arbitrarily high orders of convergence in terms of a smoothing parameter for computing spectral measures of general differential, integral, and lattice operators. Explicit pointwise and $L^p$-error bounds are derived in terms of the local regularity of the measure. We provide numerical examples, including a partial differential operator and a magnetic tight-binding model of graphene, and compute 1000 eigenvalues of a Dirac operator to near machine precision without spectral pollution. The algorithm is publicly available in SpecSolve, which is a software package written in MATLAB.

中文翻译：

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计算自伴算子的谱测度

SIAM Review，第 63 卷，第 3 期，第 489-524 页，2021 年 1 月
。我们使用解析算子开发了一种算法，用于计算与自伴随算子相关的谱测度的平滑近似值。就计算一般微分、积分和格算子的谱度量的平滑参数而言，该算法可以实现任意高阶的收敛。显式逐点和 $L^p$-误差边界是根据度量的局部规律性得出的。我们提供了数值示例，包括偏微分算子和石墨烯的磁紧束缚模型，并计算 Dirac 算子的 1000 个特征值，以接近机器精度而没有光谱污染。该算法在 SpecSolve 中公开可用，SpecSolve 是一个用 MATLAB 编写的软件包。