相关论文: SOR-like iteration and FPI are consistent when the…
The SOR-like iteration method for solving the absolute value equations~(AVE) of finding a vector $x$ such that $Ax - |x| - b = 0$ with $\nu = \|A^{-1}\|_2 < 1$ is investigated. The convergence conditions of the SOR-like iteration method…
In this paper, we reconsider two new iterative methods for solving absolute value equations (AVE), which is proposed by Ali and Pan (Jpn. J. Ind. Appl. Math. 40: 303--314, 2023). Convergence results of the two iterative schemes and new…
In this paper we propose a novel algorithm, factored value iteration (FVI), for the approximate solution of factored Markov decision processes (fMDPs). The traditional approximate value iteration algorithm is modified in two ways. For one,…
Because the expense of estimating the optimal value of the relaxation parameter in the successive over-relaxation (SOR) method is usually prohibitive, the parameter is often adaptively controlled. In this paper, new adaptive SOR methods are…
Algebraic Riccati equations (AREs) have been extensively applicable in linear optimal control problems and many efficient numerical methods were developed. The most attention of numerical solutions is the (almost) stabilizing solution in…
Many optimization algorithms$\unicode{x2013}$including gradient descent, proximal methods, and operator splitting techniques$\unicode{x2013}$can be formulated as fixed-point iterations (FPI) of continuous operators. When these operators are…
In this paper, we propose a class of matrix splitting-based fixed-point iteration (FPI) methods for solving the vertical nonlinear complementarity problem (VNCP). Under appropriate conditions, we present two convergence results obtained…
Recently, two families of HSS-based iteration methods are constructed for solving the system of absolute value equations (AVEs), which is a class of non-differentiable NP-hard problems. In this study, we establish the Picard-CSCS iteration…
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.…
The discrete-time algebraic Riccati equation (DARE) have extensive applications in optimal control problems. We provide new theoretical supports to the stability properties of solutions to the DARE and reduce the convergence conditions…
Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…
Iterative algorithms are instrumental in modern numerical simulation for solving systems arising from the discretization of PDEs. They face however significant challenges in industrial applications, such as slow convergence, limit cycle…
Randomized iterative methods, such as the Kaczmarz method and its variants, have gained growing attention due to their simplicity and efficiency in solving large-scale linear systems. Meanwhile, absolute value equations (AVE) have attracted…
Power iteration has been generalized to solve many interesting problems in machine learning and statistics. Despite its striking success, theoretical understanding of when and how such an algorithm enjoys good convergence property is…
We established a new eighth-order iterative method, consisting of three steps, for solving nonlinear equations. Per iteration the method requires four evaluations (three function evaluations and one evaluation of the first derivative).…
Stein's unbiased risk estimator (SURE) has been shown to be an effective metric for determining optimal parameters for many applications. The topic of this article is focused on the use of SURE for determining parameters for blind…
Point Group (PG) symmetries play a fundamental role in many aspects of theoretical chemistry and computational materials science. With the objective to automatize the search of PG symmetry operations of generic atomic clusters, we present a…
The ultimate goal of any numerical scheme for partial differential equations (PDEs) is to compute an approximation of user-prescribed accuracy at quasi-minimal computational time. To this end, algorithmically, the standard adaptive finite…
The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…
In this paper, an inverse-free dynamical system with fixed-time convergence is presented to solve the system of absolute value equations (AVEs). Under a mild condition, it is proved that the solution of the proposed dynamical system…