Related papers: More on Projected Type Iteration Method and Linear…
For linear systems $Ax=b$ we develop iterative algorithms based on a sketch-and-project approach. By using judicious choices for the sketch, such as the history of residuals, we develop weighting strategies that enable short recursive…
In this paper a new hp-adaptive strategy for elliptic problems based on refinement history is proposed, which chooses h-, p- or hp-refinement on individual elements according to a posteriori error estimate, as well as smoothness estimate of…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…
Matrix double splitting iterations are simple in implementation while solving real non-singular (rectangular) linear systems. In this paper, we present two Alternating Double Splitting (ADS) schemes formulated by two double splittings and…
For solving the continuous Sylvester equation, a class of the multiplicative splitting iteration method is presented. We consider two symmetric positive definite splittings for each coefficient matrix of the continuous Sylvester equations…
A new fast algebraic method for obtaining an $\mathcal{H}^2$-approximation of a matrix from its entries is presented. The main idea behind the method is based on the nested representation and the maximum-volume principle to select…
In this paper, we propose a smoothing method to solve nonlinear complementarity problems involving P 0-functions. We propose a nonparametric algorithm to solve the nonlinear corresponding system of equations and prove some global and local…
In recent years, we have established the iteration theory of the index for symplectic matrix paths and applied it to periodic solution problems of nonlinear Hamiltonian systems. This paper is a survey on these results.
The nonlinear inverse problem of exponential data fitting is separable since the fitting function is a linear combination of parameterized exponential functions, thus allowing to solve for the linear coefficients separately from the…
We study the behavior of simple principal pivoting methods for the P-matrix linear complementarity problem (P-LCP). We solve an open problem of Morris by showing that Murty's least-index pivot rule (under any fixed index order) leads to a…
We develop an iterative refinement method that improves the accuracy of a user-chosen subset of $k$ eigenvectors ($k\ll n$) of an $n\times n$ real symmetric matrix. Using an orthogonal matrix represented in compact WY form, the method…
As a continuation to our previous work [9, 10], we consider the domino tiling problem with impurities. (1) if we have more than two impurities on the boundary, we can compute the number of corresponding perfect matchings by using the…
This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
In this paper, several row and column orthogonal projection methods are proposed for solving matrix equation $AXB=C$, where the matrix $A$ and $B$ are full rank or rank deficient and equation is consistent or not. These methods are…
This paper presents an iteration method for solving linear particle transport problems in binary stochastic mixtures. It is based on nonlinear projection approach. The method is defined by a hierarchy of equations consisting of the…
A new technique for approximating the entire solution set for a nonlinear system of relations (nonlinear equations, inequalities, etc. involving algebraic, smooth, or even continuous functions) is presented. The technique is to first plot…
In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone…
In this paper, we revisit the much studied problem of Pattern Matching with Swaps (Swap Matching problem, for short). We first present a graph-theoretic model, which opens a new and so far unexplored avenue to solve the problem. Then, using…
Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system.…