Locally Optimal Block Preconditioned Conjugate Gradient Method for Hierarchical Matrices
Locally Optimal Block Preconditioned Conjugate Gradient Method for Hierarchical Matrices
复制标题
分层矩阵的局部最优分块预条件共轭梯度法
DOI：
10.1002/pamm.201110360
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
T. Mach
中科院分区：
文献类型：
--
作者：
P. Benner;T. Mach
给出了一种逼近对称自伴积分或微分算子某些(内)本征值的几乎线性复杂度的方法。利用ℋ算术，算子的离散化得到一个大的等级(ℋ)矩阵M。我们假设M是对称的，正定的。然后利用Knyazev和Neymeyr广泛研究的局部最优块预条件共轭梯度法(LOBPCG)计算最小特征值。
We present a method of almost linear complexity to approximate some (inner) eigenvalues of symmetric self‐adjoint integral or differential operators. Using ℋ‐arithmetic the discretisation of the operator leads to a large hierarchical (ℋ‐) matrix M. We assume that M is symmetric, positive definite. Then we compute the smallest eigenvalues by the locally optimal block preconditioned conjugate gradient method (LOBPCG), which has been extensively investigated by Knyazev and Neymeyr.