Related papers: Communication: Curing basis set overcompleteness w…
Electronic structure methods for accurate calculation of molecular properties have a high cost that grows steeply with the problem size, therefore, it is helpful to have the underlying atomic basis functions that are less in number but of…
We present an algorithm where only the Cholesky basis is determined in the decomposition procedure. This allows for improved screening and a partitioned matrix decomposition scheme, both of which significantly reduce memory usage and…
The modified Cholesky decomposition is commonly used for precision matrix estimation given a specified order of random variables. However, the order of variables is often not available or cannot be pre-determined. In this work, we propose…
The Cholesky decomposition is a fundamental tool for solving linear systems with symmetric and positive definite matrices which are ubiquitous in linear algebra, optimization, and machine learning. Its numerical stability can be improved by…
A new algorithm to approximate Hermitian matrices by positive semidefinite Hermitian matrices based on modified Cholesky decompositions is presented. In contrast to existing algorithms, this algorithm allows to specify bounds on the…
Large kernel systems are prone to be ill-conditioned. Pivoted Cholesky decomposition (PCD) render a stable and efficient solution to the systems without a perturbation of regularization. This paper proposes a new PCD algorithm by tuning…
Molecule-optimized basis sets, based on approximate natural orbitals, are developed for accelerating the convergence of quantum calculations with strongly correlated (multi-referenced) electrons. We use a low-cost approximate solution of…
This paper addresses the challenge of preparing mixed quantum states -- both arbitrary states in general and highly sparse ones in particular -- an area that has received far less attention than the preparation of pure states. We present…
The quantum phase estimation algorithm stands as the primary method for determining the ground state energy of a molecular electronic Hamiltonian on a quantum computer. In this context, the ability to initialize a classically tractable…
We introduce highly local basis sets for electronic structure which are very efficient for correlation calculations near the complete basis set limit. Our approach is based on gausslets, recently introduced wavelet-like smooth orthogonal…
A simple yet general method for constructing basis sets for molecular electronic structure calculations is presented. These basis sets consist of atomic natural orbitals from a multi-configurational self-consistent field calculation…
To treat the electronic structure of large molecules by electron propagator methods we developed a parallel computer program called P-RICD$\Sigma$. The program exploits the sparsity of the two-electron integral matrix by using Cholesky…
Algorithms involving Gaussian processes or determinantal point processes typically require computing the determinant of a kernel matrix. Frequently, the latter is computed from the Cholesky decomposition, an algorithm of cubic complexity in…
We propose a unique scheme to construct fully optimized atomic basis sets for density-functional calculations. The shapes of the radial functions are optimized by minimizing the {\it spillage} of the wave functions between the atomic…
We introduce the $k$-banded Cholesky prior for estimating a high-dimensional bandable precision matrix via the modified Cholesky decomposition. The bandable assumption is imposed on the Cholesky factor of the decomposition. We obtained the…
The randomly pivoted partial Cholesky algorithm (RPCholesky) computes a factorized rank-k approximation of an N x N positive-semidefinite (psd) matrix. RPCholesky requires only (k + 1) N entry evaluations and O(k^2 N) additional arithmetic…
A general procedure for the optimization of atomic density-fitting basis functions is designed with the balance between accuracy and numerical stability in mind. Given one-electron wavefunctions and energies, weights are assigned to the…
Incomplete factorizations have long been popular general-purpose algebraic preconditioners for solving large sparse linear systems of equations. Guaranteeing the factorization is breakdown free while computing a high quality preconditioner…
Density fitting (DF), also known as the resolution of the identity (RI), is a widely used technique in quantum chemical calculations with various types of atomic basis sets - Gaussian-type orbitals, Slater-type orbitals, as well as…
This work is on a user-friendly reduced basis method for solving a family of parametric PDEs by preconditioned Krylov subspace methods including the conjugate gradient method, generalized minimum residual method, and bi-conjugate gradient…