Related papers: Fast iterative solution of the Bethe-Salpeter eige…
This paper is concerned with the development and analysis of an iterative solver for high-dimensional second-order elliptic problems based on subspace-based low-rank tensor formats. Both the subspaces giving rise to low-rank approximations…
The goal of this paper is to find a low-rank approximation for a given tensor. Specifically, we give a computable strategy on calculating the rank of a given tensor, based on approximating the solution to an NP-hard problem. In this paper,…
Approximating a tensor in the tensor train (TT) format has many important applications in scientific computing. Rounding a TT tensor involves further compressing a tensor that is already in the TT format. This paper proposes new randomized…
We study efficient solution methods for stochastic eigenvalue problems arising from discretization of self-adjoint partial differential equations with random data. With the stochastic Galerkin approach, the solutions are represented as…
The predictive power of the ab initio Bethe-Salpeter equation (BSE) approach, rigorously based on many-body Green's function theory but incorporating information from density functional theory, has already been demonstrated for the optical…
In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…
Quantum eigenvalue transformation (QET) and its generalization, quantum singular value transformation (QSVT), are versatile quantum algorithms that allow us to apply broad matrix functions to quantum states, which cover many of significant…
This study focuses on addressing the challenge of solving the reduced biquaternion equality constrained least squares (RBLSE) problem. We develop algebraic techniques to derive real and complex solutions for the RBLSE problem by utilizing…
In this work, we present a method to exponentiate non-sparse indefinite low-rank matrices on a quantum computer. Given an operation for accessing the elements of the matrix, our method allows singular values and associated singular vectors…
The problem of recovering a low-rank matrix from the linear constraints, known as affine matrix rank minimization problem, has been attracting extensive attention in recent years. In general, affine matrix rank minimization problem is a…
The $GW$-Bethe-Salpeter Equation (BSE) method is promising for calculating the low-lying excited states of molecular systems. So far, it has only been applied to rather small molecules, and in the commonly implemented diagonal…
The numerical solution of kinetic equations is challenging due to the high dimensionality of the underlying phase space. In this paper, we develop a dynamical low-rank method based on the projector-splitting integrator in tensor-train (TT)…
In symmetric block eigenvalue algorithms, such as the subspace iteration algorithm and the locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm, a large block size is often employed to achieve robustness and rapid…
We consider an approximate computation of several minimal eigenpairs of large Hermitian matrices which come from high--dimensional problems. We use the tensor train format (TT) for vectors and matrices to overcome the curse of…
This paper proposes a novel formulation of the tensor completion problem to impute missing entries of data represented by tensors. The formulation is introduced in terms of tensor train (TT) rank which can effectively capture global…
The radiative transfer equation (RTE) has been established as a fundamental tool for the description of energy transport, absorption and scattering in many relevant societal applications, and requires numerical approximations. However,…
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…
Low-rank Tucker and CP tensor decompositions are powerful tools in data analytics. The widely used alternating least squares (ALS) method, which solves a sequence of over-determined least squares subproblems, is costly for large and sparse…
Recovery of low-rank matrices has recently seen significant activity in many areas of science and engineering, motivated by recent theoretical results for exact reconstruction guarantees and interesting practical applications. A number of…
Variational Quantum algorithms, especially Quantum Approximate Optimization and Variational Quantum Eigensolver (VQE) have established their potential to provide computational advantage in the realm of combinatorial optimization. However,…