Related papers: Matrix Structure Exploitation in Generalized Eigen…
We propose a new iterative algorithm for generating a subset of eigenvalues and eigenvectors of large matrices which generalizes the method of optimal relaxations. We also give convergence criteria for the iterative process, investigate its…
Hierarchical matrices approximate a given matrix by a decomposition into low-rank submatrices that can be handled efficiently in factorized form. $\mathcal{H}^2$-matrices refine this representation following the ideas of fast multipole…
We investigate numerically efficient approximations of eigenspaces associated to symmetric and general matrices. The eigenspaces are factored into a fixed number of fundamental components that can be efficiently manipulated (we consider…
In this paper, we obtain improved running times for regression and top eigenvector computation for numerically sparse matrices. Given a data matrix $A \in \mathbb{R}^{n \times d}$ where every row $a \in \mathbb{R}^d$ has $\|a\|_2^2 \leq L$…
Dual decomposition provides a tractable framework for designing algorithms for finding the most probable (MAP) configuration in graphical models. However, for many real-world inference problems, the typical decomposition has a large…
A large number of computational and scientific methods commonly require decomposing a sparse matrix into triangular factors as LU decomposition. A common problem faced during this decomposition is that even though the given matrix may be…
In this work we present a new method for basis set generation for electronic structure calculations of crystalline solids. This procedure is aimed at applications to Density Functional Theory (DFT). In this construction, Energy Window…
We investigate solutions to the functional equation $f(f(x)) = e^x$, which can be interpreted as the problem of finding a half iterate of the exponential map. While no elementary solution exists, we construct and analyze non-elementary…
This article addresses a fundamental problem faced by the ab initio community: the lack of an effective formalism for the rapid exploration and exchange of new methods. To rectify this, we introduce a novel, basis-set independent,…
Large biomolecular systems, whose function may involve thousands of atoms, cannot easily be addressed with parameter-free density functional theory (DFT) calculations. Until recently a central problem was that such systems possess an…
Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. However, this effort involves repeatedly diagonalizing…
Recently we proposed an information entropy based method for electronic structure calculations within the density-matrix functional theory(DMFT) (Phys. Rev. Lett. 128, 013001), dubbed as $i$-DMFT. Comments have been raised regarding the…
Real time, density matrix based, time dependent density functional theory proceeds through the propagation of the density matrix, as opposed to the Kohn-Sham orbitals. It is possible to reduce the computational workload by imposing spatial…
One of the central problems in quantum mechanics is to determine the ground state properties of a system of electrons interacting via the Coulomb potential. Since its introduction by Hohenberg, Kohn, and Sham, Density Functional Theory…
Although density functional theory (DFT) has aided in accelerating the discovery of new materials, such calculations are computationally expensive, especially for high-throughput efforts. This has prompted an explosion in exploration of…
The article presents a computationally effective algorithm for calculating the multiresolution discrete Fourier transform (MrDFT). The algorithm is based on the idea of reducing the computational complexity which was introduced by Wen and…
We present an algorithm and its parallel implementation for solving a self consistent problem as encountered in Hartree Fock or Density Functional Theory. The algorithm takes advantage of the sparsity of matrices through the use of local…
Feature Transformation is crucial for classic machine learning that aims to generate feature combinations to enhance the performance of downstream tasks from a data-centric perspective. Current methodologies, such as manual expert-driven…
This note considers the unstructured sparse recovery problems in a general form. Examples include rational approximation, spectral function estimation, Fourier inversion, Laplace inversion, and sparse deconvolution. The main challenges are…
A new O(N) algorithm based on a recursion method, in which the computational effort is proportional to the number of atoms N, is presented for calculating the inverse of an overlap matrix which is needed in electronic structure calculations…