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.

翻译：提出了一种新型的无孔化方法以及两种具体的算法来解决极端的精度值问题。除了基于梯度的算法外,提议的算法还修改了多柱梯度,使以前的列与后面的列脱钩。几乎可以肯定地保证全球趋同与源体而非源空间的趋同。从当地来看,算法依eigengaps的线性趋同率而线性趋同率趋同。将动力加速、精确的线搜索和柱子锁定结合在一起,以进一步加速两种算法,并降低计算成本。我们用不同频谱分布的多个随机矩阵和计算化学的矩阵展示了这两种算法的效率。