Iterative methods for computing vibrational spectra
type: Item
instance of: scholarly article
title: Iterative methods for computing vibrational spectra
published in: Mathematics
publication date: 2018-08-13T00:00:00Z
review text: Summary: I review some computational methods for calculating vibrational spectra. They all use iterative eigensolvers to compute eigenvalues of a Hamiltonian matrix by evaluating matrix-vector products (MVPs). A direct-product basis can be used for molecules with five or fewer atoms. This is done by exploiting the structure of the basis and the structure of a direct product quadrature grid. I outline three methods that can be used for molecules with more than five atoms. The first uses contracted basis functions and an intermediate \((\mathbf F)\) matrix. The second uses Smolyak quadrature and a pruned basis. The third uses a tensor rank reduction scheme.
Mathematics Subject Classification ID: 65-XX
Mathematics Subject Classification ID: 15-XX
Mathematics Subject Classification ID: 94-XX
zbMATH DE Number: 6916888
zbMATH Keywords: vibrational spectroscopy
zbMATH Keywords: iterative eigensolvers
zbMATH Keywords: contracted basis functions
zbMATH Keywords: Smolyak grids
zbMATH Keywords: rank reduction
author: Tucker jun. Carrington
describes a project that uses: MCTDH
describes a project that uses: ARPACK
describes a project that uses: TROVE
MaRDI profile type: Publication
full work available at URL: math6010013
OpenAlex ID: W2788615233
cites work: Q4917542
cites work: General foundations of high-dimensional model representations
cites work: Fast calculation of coefficients in the Smolyak algorithm
cites work: Rank-one approximation to high order tensors
cites work: Numerical operator calculus in higher dimensions
cites work: Algorithms for Numerical Analysis in High Dimensions
cites work: ARPACK Users' Guide
DOI: 10.3390/MATH6010013
description: scientific article; zbMATH DE number 6916888