Convergence Analysis of Direct Minimization and Self-Consistent Iterations
From MaRDI portal
Publication:5857844
DOI10.1137/20M1332864zbMath1467.65054arXiv2004.09088OpenAlexW3133725437MaRDI QIDQ5857844
Gaspard Kemlin, Eric Cancès, Antoine Levitt
Publication date: 8 April 2021
Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2004.09088
density matricesself-consistent field methodelectronic structuredirect minimization methodmathematical quantum chemistry
Numerical optimization and variational techniques (65K10) Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17)
Related Items
Convergent and Orthogonality Preserving Schemes for Approximating the Kohn-Sham Orbitals ⋮ Stochastic algorithms for self-consistent calculations of electronic structures ⋮ Energy-adaptive Riemannian optimization on the Stiefel manifold ⋮ Implicit algorithms for eigenvector nonlinearities ⋮ Practical Error Bounds for Properties in Plane-Wave Electronic Structure Calculations ⋮ A robust and efficient line search for self-consistent field iterations ⋮ Body-ordered approximations of atomic properties ⋮ An overview of \textit{a posteriori} error estimation and post-processing methods for nonlinear eigenvalue problems ⋮ The dependency of spectral gaps on the convergence of the inverse iteration for a nonlinear eigenvector problem ⋮ Variational Characterization of Monotone Nonlinear Eigenvector Problems and Geometry of Self-Consistent Field Iteration ⋮ Numerical stability and efficiency of response property calculations in density functional theory ⋮ A Quasi-Optimal Factorization Preconditioner for Periodic Schrödinger Eigenstates in Anisotropically Expanding Domains
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A projected preconditioned conjugate gradient algorithm for computing many extreme eigenpairs of a Hermitian matrix
- Numerical analysis of nonlinear eigenvalue problems
- An analysis for the DIIS acceleration method used in quantum chemistry calculations
- Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by preconditioned nonlinear conjugate gradient methods
- Perturbation theory for linear operators.
- Mathematical theory and numerical methods for Bose-Einstein condensation
- A density matrix approach to the convergence of the self-consistent field iteration
- Convergence of gradient-based algorithms for the Hartree-Fock equations
- Numerical analysis of the planewave discretization of some orbital-free and Kohn-Sham models
- Gradient Type Optimization Methods For Electronic Structure Calculations
- On the Convergence of the Self-Consistent Field Iteration in Kohn--Sham Density Functional Theory
- The density matrix in self-consistent field theory I. Iterative construction of the density matrix
- Preconditioned gradient flows for nonlinear eigenvalue problems and application to the Hartree-Fock functional
- On the Convergence of the Self-Consistent Field Iteration for a Class of Nonlinear Eigenvalue Problems
- The Geometry of Algorithms with Orthogonality Constraints
- On the convergence of SCF algorithms for the Hartree-Fock equations
- Computation of Ground States of the Gross--Pitaevskii Functional via Riemannian Optimization
- A Conjugate Gradient Method for Electronic Structure Calculations
- Computing the Ground State Solution of Bose--Einstein Condensates by a Normalized Gradient Flow
- Sobolev Gradient Flow for the Gross--Pitaevskii Eigenvalue Problem: Global Convergence and Computational Efficiency
- Numerical Methods for Electronic Structure Calculations of Materials
- Numerical methods for Kohn–Sham density functional theory
- A Mathematical Introduction to Electronic Structure Theory
- A Riemannian Newton Algorithm for Nonlinear Eigenvalue Problems
- Functions of Matrices
- On the Analysis of the Discretized Kohn--Sham Density Functional Theory
- Electronic Structure
- A Formula for the Spectral Radius of an Operator
- New Developments in Molecular Orbital Theory