Reduced‐cost sparsity‐exploiting algorithm for solving coupled‐cluster equations. Issue 12 (24th January 2016)

• Record Type: Journal Article
• Authors: Brabec, Jiri; Yang, Chao; Epifanovsky, Evgeny; Krylov, Anna I.; Ng, Esmond
• Is Part Of: Journal of computational chemistry. Volume 37:Issue 12(2016)
• Page Start: 1059
• Page End: 1067
• Publication Date: 2016-01-24
• Subjects: coupled‐cluster methods -- sparsity -- sparse correction -- quasi‐Newton -- solvers; Chemistry -- Data processing -- Periodicals; 542.85
• DOI: 10.1002/jcc.24293
• Languages: English
• ISSNs: 0192-8651

Abstract

Abstract : We present an algorithm for reducing the computational work involved in coupled‐cluster (CC) calculations by sparsifying the amplitude correction within a CC amplitude update procedure. We provide a theoretical justification for this approach, which is based on the convergence theory of inexact Newton iterations. We demonstrate by numerical examples that, in the simplest case of the CCD equations, we can sparsify the amplitude correction by setting, on average, roughly 90% nonzero elements to zeros without a major effect on the convergence of the inexact Newton iterations. Abstract : By sparsifying the amplitude correction to approximate solutions to the coupled‐cluster amplitude equations, the number of operations in the tensor contraction performed in the inexact Newton algorithm can be significantly reduced. Nearly, the same convergence rate is maintained even when roughly 90% of nonzero elements in the amplitude correction are set to zero (i.e., z = 10%).