论文标题
用于解决极端特征值问题的三角形矫正方法
Triangularized Orthogonalization-free Method for Solving Extreme Eigenvalue Problems
论文作者
论文摘要
提出了一种新型的无矫正方法以及两种特定算法来解决极端的特征值问题。除了基于梯度的算法之外，所提出的算法修改了多列梯度，以使早期的列与后来的列解耦合。几乎可以肯定地保证了全球融合特征向量而不是本征空间。在局部，算法根据特征，与收敛速率线性收敛。并入动量加速度，精确线路搜索和列锁定，以进一步加速这两种算法并降低其计算成本。我们证明了两种算法在几个随机矩阵上具有不同频谱分布和计算化学矩阵的效率。
A novel orthogonalization-free method together with two specific algorithms are proposed to solve extreme eigenvalue problems. On top of gradient-based algorithms, the proposed algorithms modify the multi-column gradient such that earlier columns are decoupled from later ones. Global convergence to eigenvectors instead of eigenspace is guaranteed almost surely. Locally, algorithms converge linearly with convergence rate depending on eigengaps. Momentum acceleration, exact linesearch, and column locking are incorporated to further accelerate both algorithms and reduce their computational costs. We demonstrate the efficiency of both algorithms on several random matrices with different spectrum distribution and matrices from computational chemistry.
