Theoretical and computational improvements to the algebraic method for discovering cooperative rigid‐unit modes. Issue 6 (2nd November 2021)

• Record Type: Journal Article
• Authors: Campbell, Branton J.; Stokes, Harold T.; Averett, Tyler B.; Machlus, Shae; Yost, Christopher J.
• Is Part Of: Journal of applied crystallography. Volume 54:Issue 6(2021)
• Page Start: 1664
• Page End: 1675
• Publication Date: 2021-11-02
• Subjects: rigid‐unit modes -- symmetry modes -- group representation theory -- singular value decomposition -- Gaussian elimination; Crystallography -- Periodicals; 548.05
• DOI: 10.1107/S1600576721009341
• Languages: English
• ISSNs: 0021-8898

Abstract

Abstract : The linear‐algebraic approach to finding cooperative rigid‐unit modes in interconnected networks has been greatly improved. Abstract : A linear‐algebraic algorithm for identifying rigid‐unit modes in networks of interconnected rigid units has recently been demonstrated. This article presents a series of enhancements to the original algorithm, which greatly improve its conceptual simplicity, numerical robustness, computational efficiency and interpretability. The improvements include the efficient isolation of constraints, the observation of variable‐block separability, the use of singular value decomposition and a quantitative measure of solution inexactness.