相关论文: Deflated Iterative Methods for Linear Equations wi…
The isomonodromy deformation method is applied to the scaling limits in the linear NxN matrix equations with rational coefficients to obtain the deformation equations for the algebraic curves which describe the local behavior of the reduced…
A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…
We study the GMRES algorithm applied to linear systems of equations involving a scaled and shifted $N\times N$ matrix whose entries are independent complex Gaussians. When the right hand side of this linear system is independent of this…
In this work we are interested in general linear inverse problems where the corresponding forward problem is solved iteratively using fixed point methods. Then one-shot methods, which iterate at the same time on the forward problem solution…
A simple iteration methodology for the solution of a set of a linear algebraic equations is presented. The explanation of this method is based on a pure geometrical interpretation and pictorial representation. Convergence using this method…
This article introduces a new fast direct solver for linear systems arising out of wide range of applications, integral equations, multivariate statistics, radial basis interpolation, etc., to name a few. \emph{The highlight of this new…
In this note we aim at putting more emphasis on the fact that trying to solve non-convex optimization problems with coordinate-descent iterative linear matrix inequality algorithms leads to suboptimal solutions, and put forward other…
Gradient methods have applications in multiple fields, including signal processing, image processing, and dynamic systems. In this paper, we present a nonlinear gradient method for solving convex supra-quadratic functions by developing the…
This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…
We consider efficient methods for computing solutions to dynamic inverse problems, where both the quantities of interest and the forward operator (measurement process) may change at different time instances but we want to solve for all the…
Among the methods for solving ODE-IVPs, the class of General Linear Methods (GLMs) is able to encompass most of them, ranging from Linear Multistep Formulae (LMF) to RK formulae. Moreover, it is possible to obtain methods able to overcome…
For solving linear ill-posed problems regularization methods are required when the right hand side is with some noise. In the present paper regularized solutions are obtained by implicit iteration methods in Hilbert scales. % By exploiting…
We develop a high-order hybridized discontinuous Galerkin (HDG) method for a linear degenerate elliptic equation arising from a two-phase mixture of mantle convection or glacier dynamics. We show that the proposed HDG method is well-posed…
This paper presents a brief historical survey of iterative methods for solving linear systems of equations. The journey begins with Gauss who developed the first known method that can be termed iterative. The early 20th century saw good…
Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
Employing two distinct types of regularization terms, we propose two regularized extragradient methods for solving equilibrium problems on Hadamard manifolds. The sequences generated by these extragradient algorithms converge to a solution…
We develop an accelerated gradient descent algorithm on the Grassmann manifold to compute the subspace spanned by a number of leading eigenvectors of a symmetric positive semi-definite matrix. This has a constant cost per iteration and a…
We propose an iterative finite element method for solving non-linear hydromagnetic and steady Euler's equations. Some three-dimensional computational tests are given to confirm the convergence and the high efficiency of the method.
We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract…