Computing Spectral Measures of Self-Adjoint Operators
Computing Spectral Measures of Self-Adjoint Operators
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DOI：
10.1137/20m1330944
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发表时间：
2021-09-01
期刊：
影响因子：
10.2
通讯作者：
Townsend, Alex
中科院分区：
文献类型：
--
作者：
Colbrook, Matthew;Horning, Andrew;Townsend, Alex
使用预解算子，我们开发了一个算法计算与自伴算子相关的谱测度的光滑近似。该算法可以实现任意高阶的收敛性的光滑参数计算谱措施的一般微分，积分和格算子。显式逐点和L-p-误差界的措施，根据当地的正则性。我们提供了数值例子，包括偏微分算子和磁紧束缚模型的石墨烯，并计算1000狄拉克算子的特征值，以接近机器的精度，没有光谱污染。该算法在SpecSolve中公开，这是一个用MATLAB编写的软件包。
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.