相关论文: An efficient algorithm for Cholesky decomposition …

We present a reduced-scaling auxiliary-field quantum Monte Carlo (AFQMC) framework designed for large molecular systems and ensembles, with or without coupling to optical cavities. Our approach leverages the natural block sparsity of…

The orthogonalization process is an essential building block in Krylov space methods, which takes up a large portion of the computational time. Commonly used methods, like the Gram-Schmidt method, consider the projection and normalization…

We propose a linear-time algorithm to compute low-rank Chow decompositions. Our algorithm can decompose concise symmetric 3-tensors in n variables of Chow rank n/3. The algorithm is pencil based, hence it relies on generalized eigenvalue…

We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…

An iterative method is derived for image reconstruction. Among other attributes, this method allows constraints unrelated to the radiation measurements to be incorporated into the reconstructed image. A comparison is made with the widely…

We construct a new error-suppression scheme that makes use of the adjoint of reversible quantum algorithms. For decoherence induced errors such as depolarization, it is presented that provided the depolarization error probability is less…

In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, Gaussian processes (GPs) and kernel methods have garnered…

When given a generalized matrix separation problem, which aims to recover a low rank matrix $L_0$ and a sparse matrix $S_0$ from $M_0=L_0+HS_0$, the work \cite{CW25} proposes a novel convex optimization problem whose objective function is…

Application of real-time matrix algorithm in heavy ion induced complete fusion nuclear reactions of superheavy elements synthesis is reviewed in brief. An extended algorithm, for the case of the recoil detection efficiency is not close to…

The solution of sparse symmetric positive definite linear systems is an important computational kernel in large-scale scientific and engineering modeling and simulation. We will solve the linear systems using a direct method, in which a…

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…

Many important real-world applications, such as System Identification with Gaussian Processes, involve solving linear systems with symmetric positive-definite matrices. The iterative CG method and direct solvers based on the Cholesky…

Cholesky factorization is a widely used method for solving linear systems involving symmetric, positive-definite matrices, and can be an attractive choice in applications where a high degree of numerical stability is needed. One such…

A fast non-convex low-rank matrix decomposition method for potential field data separation is proposed. The singular value decomposition of the large size trajectory matrix, which is also a block Hankel matrix, is obtained using a fast…

We present a fast algorithm to calculate Coulomb/exchange integrals of prolate spheroidal electronic orbitals, which are the exact solutions of the single-electron, two-center Schr\"odinger equation for diatomic molecules. Our approach…

Many neural learning algorithms require to solve large least square systems in order to obtain synaptic weights. Moore-Penrose inverse matrices allow for solving such systems, even with rank deficiency, and they provide minimum-norm vectors…

In this paper we propose a new inexact dual decomposition algorithm for solving separable convex optimization problems. This algorithm is a combination of three techniques: dual Lagrangian decomposition, smoothing and excessive gap. The…

We present a new sink particle algorithm developed for the Adaptive Mesh Refinement code RAMSES. Our main addition is the use of a clump finder to identify density peaks and their associated regions (the peak patches). This allows us to…

A methodology to reduce the computational cost of time domain computations of eddy currents problems is proposed and implemented in a parallel computing environment. It is based on the modal decomposition of the current density and it is…

We present an efficient algorithm for one- and two-component relativistic exact-decoupling calculations. Spin-orbit coupling is thus taken into account for the evaluation of relativistically transformed (one-electron) Hamiltonian. As the…