Rational iterative methods for the matrix sign function
SIAM Journal on Matrix Analysis and Applications
A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
Matrix computations (3rd ed.)
Fast spectral projection algorithms for density-matrix computations
Journal of Computational Physics
Multilevel domain decomposition for electronic structure calculations
Journal of Computational Physics
Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics)
Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics)
SIAM Journal on Matrix Analysis and Applications
Hi-index | 0.00 |
Recursive Fermi-Dirac operator expansion is an efficient way to compute one-electron density matrices in electronic structure theory. The convergence is rapid and depends only weakly on the conditioning of the problem and, for many systems, the computational cost increases only linearly with system size. In this article, errors introduced when evaluating the recursive expansion are analyzed and schemes to control the forward error are proposed. The error has previously been analyzed for explicit schemes working at zero electronic temperature [J. Chem. Phys., 128 (2008), 074106]. Here, implicit schemes [Phys. Rev. B, 68 (2003), 233104] working at zero or finite temperature are treated. The proposed schemes for error control are demonstrated by tight-binding as well as density functional theory electronic structure calculations on several test systems. Condition numbers for the problem of computing the density matrix are derived, giving quantitative insight into under what circumstances a temperature dependent formulation results in better conditioning. It is shown that for the considered recursive expansions, the number of matrix-matrix multiplications needed to compute the density matrix increases only with the squared logarithm of the condition number of the problem.