Related papers: Lopsided HSS Iterative Method and Preconditioner f…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
The paper introduces the sweeping preconditioner, which is highly efficient for iterative solutions of the variable coefficient Helmholtz equation including very high frequency problems. The first central idea of this novel approach is to…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
A new method, the Dynamical Systems Method (DSM), justified recently, is applied to solving ill-conditioned linear algebraic system (ICLAS). The DSM gives a new approach to solving a wide class of ill-posed problems. In this paper a new…
Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning multivariate time series. However, in general, it is difficult to set the dimension of its hidden state space. A small number of hidden states may…
Linear regression in $\ell_p$-norm is a canonical optimization problem that arises in several applications, including sparse recovery, semi-supervised learning, and signal processing. Generic convex optimization algorithms for solving…
Iterative methods based on tensors have emerged as powerful tools for solving tensor equations, and have significantly advanced across multiple disciplines. In this study, we propose two-step tensor-based iterative methods to solve the…
Presented in this paper is a new sparse linear solver methodology motivated by multigrid principles and based around general local transformations that diagonalize a matrix while maintaining its sparsity. These transformations are…
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…
High dimensional sparse learning has imposed a great computational challenge to large scale data analysis. In this paper, we are interested in a broad class of sparse learning approaches formulated as linear programs parametrized by a {\em…
Preconditioners are generally essential for fast convergence in the iterative solution of linear systems of equations. However, the computation of a good preconditioner can be expensive. So, while solving a sequence of many linear systems,…
In this paper we construct and analyse a level-dependent coarsegrid correction scheme for indefinite Helmholtz problems. This adapted multigrid method is capable of solving the Helmholtz equation on the finest grid using a series of…
Based on the Scale-Splitting (SCSP) iteration method presented by Hezari et al. in (A new iterative method for solving a class of complex symmetric system linear of equations, Numerical Algorithms 73 (2016) 927-955), we present a new…
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…
We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…
This paper introduces a new sweeping preconditioner for the iterative solution of the variable coefficient Helmholtz equation in two and three dimensions. The algorithms follow the general structure of constructing an approximate $LDL^t$…
In this paper, we show that simple {Stochastic} subGradient Decent methods with multiple Restarting, named {\bf RSGD}, can achieve a \textit{linear convergence rate} for a class of non-smooth and non-strongly convex optimization problems…
Multistep matrix splitting iterations serve as preconditioning for Krylov subspace methods for solving singular linear systems. The preconditioner is applied to the generalized minimal residual (GMRES) method and the flexible GMRES (FGMRES)…
We present a class of reduced basis (RB) methods for the iterative solution of parametrized symmetric positive-definite (SPD) linear systems. The essential ingredients are a Galerkin projection of the underlying parametrized system onto a…
When solving linear systems with nonsymmetric Toeplitz or multilevel Toeplitz matrices using Krylov subspace methods, the coefficient matrix may be symmetrized. The preconditioned MINRES method can then be applied to this symmetrized…