Related papers: Asynchronous iterations of HSS method for non-Herm…
We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with relatively small number of negative eigenvalues. The proposed…
A linearly implicit conservative difference scheme is applied to discretize the attractive coupled nonlinear Schr\"odinger equations with fractional Laplacian. Complex symmetric linear systems can be obtained, and the system matrices are…
Linear autoregressive models serve as basic representations of discrete time stochastic processes. Different attempts have been made to provide non-linear versions of the basic autoregressive process, including different versions based on…
The indefinite least squares (ILS) problem is a generalization of the famous linear least squares problem. It minimizes an indefinite quadratic form with respect to a signature matrix. For this problem, we first propose an impressively…
Salkuyeh proposed the Picard-HSS iteration method to solve the absolute value equation (AVE), which is a class of non-differentiable NP-hard problem. To further improve its performance, a nonlinear HSS-like iteration method is proposed.…
Given a sparse Hermitian matrix $A$ and a real number $\mu$, we construct a set of sparse vectors, each approximately spanned only by eigenvectors of $A$ corresponding to eigenvalues near $\mu$. This set of vectors spans the column space of…
We generalize classical results in spectral graph theory and linear algebra more broadly, from the case where the underlying matrix is Hermitian to the case where it is non-Hermitian. New admissibility conditions are introduced to replace…
Recently, a so-called E-MS algorithm was developed for model selection in the presence of missing data. Specifically, it performs the Expectation step (E step) and Model Selection step (MS step) alternately to find the minimum point of the…
Hidden semi-Markov Models (HSMM's) - while broadly in use - are restricted to a discrete and uniform time grid. They are thus not well suited to explain often irregularly spaced discrete event data from continuous-time phenomena. We show…
We analyze an algorithm for computing a skew-Hermitian logarithm of a unitary matrix. This algorithm is very easy to implement using standard software and it works well even for unitary matrices with no spectral conditions assumed. Certain…
We propose a hierarchical splitting approach to differential equations that provides a design principle for constructing splitting methods for $N$-split systems by iteratively applying splitting methods for two-split systems. We analyze the…
While distributed training significantly speeds up the training process of the deep neural network (DNN), the utilization of the cluster is relatively low due to the time-consuming data synchronizing between workers. To alleviate this…
Parallel trajectory optimization via the Alternating Direction Method of Multipliers (ADMM) has emerged as a scalable approach to long-horizon motion planning. However, existing frameworks typically decompose the problem into parallel…
We study simultaneous inference for multiple matrix-variate Gaussian graphical models in high-dimensional settings. Such models arise when spatiotemporal data are collected across multiple sample groups or experimental sessions, where each…
We present a new iterative rotation inversion technique based on the Simultaneous Algebraic Reconstruction Technique developed for image reconstruction. We describe in detail our algorithmic implementation and compare it to the classical…
In this paper we propose a fast optimization algorithm for approximately minimizing convex quadratic functions over the intersection of affine and separable constraints (i.e., the Cartesian product of possibly nonconvex real sets). This…
Recent development on mixed precision techniques has largely enhanced the performance of various linear algebra solvers, one of which being the solver for the least squares problem $\min_{x}\lVert b-Ax\rVert_{2}$. By transforming least…
A Gaussian process (GP) is a powerful and widely used regression technique. The main building block of a GP regression is the covariance kernel, which characterizes the relationship between pairs in the random field. The optimization to…
Studying the optoelectronic structure of materials can require the computation of several thousands of the smallest positive eigenpairs of a pseudo-hermitian Hamiltonian. Iterative eigensolvers may be preferred over direct methods for this…
Neural network solvers represent an innovative and promising approach for tackling time-fractional partial differential equations by utilizing deep learning techniques. L1 interpolation approximation serves as the standard method for…