Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 93, Issue 3, Pages -Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-022-02025-0
Keywords
Eigenvalue problem; Orthogonalization-free; Iterative eigensolver; Full configuration interaction; 65CF52
Categories
Funding
- National Key R&D Program of China [2020YFA0711900, 2020YFA0711902]
- National Natural Science Foundation of China [12271109]
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A novel orthogonalization-free method, along with two specific algorithms, is proposed to address extreme eigenvalue problems. Both algorithms converge linearly at the local level, with convergence rates depending on eigengaps. Additional measures, such as momentum acceleration, exact linesearch, and column locking, are incorporated to accelerate algorithms and reduce computational costs.
A novel orthogonalization-free method together with two specific algorithms is proposed to address extreme eigenvalue problems. On top of gradient-based algorithms, the proposed algorithms modify the multicolumn gradient such that earlier columns are decoupled from later ones. Locally, both algorithms converge linearly with convergence rates depending on eigengaps. Momentum acceleration, exact linesearch, and column locking are incorporated to accelerate algorithms and reduce their computational costs. We demonstrate the efficiency of both algorithms on random matrices with different spectrum distributions and matrices from computational chemistry.
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