相关论文: On the preconditioned AOR iterative method for Z-m…
Polynomial convergence bounds are considered for left, right, and split preconditioned GMRES. They include the cases of Weighted and Deflated GMRES for a linear system Ax = b. In particular, the case of positive definite A is considered.…
Preconditioned Krylov subspace (KSP) methods are widely used for solving large-scale sparse linear systems arising from numerical solutions of partial differential equations (PDEs). These linear systems are often nonsymmetric due to the…
This paper presents iterative methods for solving tensor equations involving the T-product. The proposed approaches apply tensor computations without matrix construction. For each initial tensor, these algorithms solve related problems in a…
This study concerns the fast and accurate solution of the line radiation transfer problem, under non-LTE conditions. We propose and evaluate an alternative iterative scheme to the classical ALI-Jacobi method, and to the more recently…
Tensor networks are a class of algorithms aimed at reducing the computational complexity of high-dimensional problems. They are used in an increasing number of applications, from quantum simulations to machine learning. Exploiting data…
We consider using the preconditioned-Krylov subspace method to solve the system of linear equations with a three-by-three block structure. By making use of the three-by-three block structure, eight inexact block factorization…
The convergence rates of iterative methods for solving a linear system $\mathbf{A} x = b$ typically depend on the condition number of the matrix $\mathbf{A}$. Preconditioning is a common way of speeding up these methods by reducing that…
We are concerned with the tensor equation with an M-tensor or Z-tensor, which we call the M- tensor equation or Z-tensor equation respectively. We derive a necessary and sufficient condition for a Z (or M)-tensor equation to have…
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
By viewing non-commutative polynomials, that is, elements in free associative algebras, in terms of linear representations, we generalize Horner's rule to the non-commutative (multivariate) setting. We introduce the concept of Horner…
We aim to solve the incompressible Navier-Stokes equations within the complex microstructure of a porous material. Discretizing the equations on a fine grid using a staggered (e.g., marker-and-cell, mixed FEM) scheme results in a nonlinear…
Prior to the parallel solution of a large linear system, it is required to perform a partitioning of its equations/unknowns. Standard partitioning algorithms are designed using the considerations of the efficiency of the parallel…
When iteratively solving linear systems By=b with Hermitian positive semi-definite $B$, and in particular when solving least-squares problems for $Ax=b$ by reformulating them as $AA^\ast y=b$, it is often observed that SOR-type methods…
A primary computational problem in kernel regression is solution of a dense linear system with the $N\times N$ kernel matrix. Because a direct solution has an O($N^3$) cost, iterative Krylov methods are often used with fast matrix-vector…
This paper presents a case study of application of the preconditioned method of conjugate gradients (CG) on a problem with operator resembling the structure of sum of Kronecker products. In particular, we are solving the Poisson's equation…
Phase-field fracture models lead to variational problems that can be written as a coupled variational equality and inequality system. Numerically, such problems can be treated with Galerkin finite elements and primal-dual active set…
We propose fast O(N) preconditioning, where N is the number of gridpoints on the prediction horizon, for iterative solution of (non)-linear systems appearing in model predictive control methods such as forward-difference Newton-Krylov…
Gaussian process hyperparameter optimization requires linear solves with, and log-determinants of, large kernel matrices. Iterative numerical techniques are becoming popular to scale to larger datasets, relying on the conjugate gradient…
Using the framework of operator or Calder\'on preconditioning, uniform preconditioners are constructed for elliptic operators discretized with continuous finite (or boundary) elements. The preconditioners are constructed as the composition…
The method of this paper is my original creation. A new method for solving linear differential equations is proposed in this paper. The important conclusion of this paper is that arbitrary order linear ordinary differential equations with…