论文标题
自我伴侣运算符的计算频谱测量
Computing spectral measures of self-adjoint operators
论文作者
论文摘要
使用分解运算符，我们开发了一种用于计算与自动接合运算符相关的光谱测量近似值的算法。该算法可以在计算一般差异，积分和晶格运算符的计算光谱测量的平滑参数方面任意获得收敛的高端口。明确的点和$ l^p $ -Error边界是根据措施的本地规则性得出的。我们提供数值示例，包括部分差分运算符，石墨烯的磁性紧密结合模型，并将狄拉克操作员的一千个特征值计算为无光谱污染的近机精度。该算法在$ \ texttt {specsolve} $中公开可用，该软件包用MATLAB编写。
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, a magnetic tight-binding model of graphene, and compute one thousand eigenvalues of a Dirac operator to near machine precision without spectral pollution. The algorithm is publicly available in $\texttt{SpecSolve}$, which is a software package written in MATLAB.
