论文标题
K $ω$ - 换移的Krylov子空间方法的开源库$（zi-h）x = b $
K$ω$ -- Open-source library for the shifted Krylov subspace method of the form $(zI-H)x=b$
论文作者
论文摘要
我们开发了K $ω$，这是一个用于转移的Krylov子空间方法的开源线性代数库。该方法求解一组移动的线性方程$（z_k i-h）x^{（k）} = b \，（k = 0,1,2，...）$ for给定矩阵$ h $和vector $ b $，同时。操作成本的领先顺序与单个方程式相同。 Krylov子空间的移位不变性是转移的Krylov子空间方法的数学基础。提出了材料科学中的应用，以证明算法比标准的Krylov子空间方法（例如兰斯佐斯方法）的优势。我们介绍了（i）激发（光学）频谱和（ii）中间特征值的基准计算。结合量子晶格求解器$ \ MATHCAL {H}φ$，K $ω$可以实现各种量子晶格模型的激发光谱和中间特征值的平行计算。
We develop K$ω$, an open-source linear algebra library for the shifted Krylov subspace methods. The methods solve a set of shifted linear equations $(z_k I-H)x^{(k)}=b\, (k=0,1,2,...)$ for a given matrix $H$ and a vector $b$, simultaneously. The leading order of the operational cost is the same as that for a single equation. The shift invariance of the Krylov subspace is the mathematical foundation of the shifted Krylov subspace methods. Applications in materials science are presented to demonstrate the advantages of the algorithm over the standard Krylov subspace methods such as the Lanczos method. We introduce benchmark calculations of (i) an excited (optical) spectrum and (ii) intermediate eigenvalues by the contour integral on the complex plane. In combination with the quantum lattice solver $\mathcal{H} Φ$, K$ω$ can realize parallel computation of excitation spectra and intermediate eigenvalues for various quantum lattice models.
