Related papers: Comments on finite termination of the generalized …
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…
An inexact framework of the Newton-based matrix splitting (INMS) iterative method is developed to solve the generalized absolute value equation, whose exact version was proposed by Zhou, Wu and Li [H.-Y. Zhou, S.-L. Wu and C.-X. Li,…
This paper proposes a Newton-type method to solve numerically the eigenproblem of several diagonalizable matrices, which pairwise commute. A classical result states that these matrices are simultaneously diagonalizable. From a suitable…
In this paper, we first propose a new parameterized definition of comparison matrix of a given complex matrix, which generalizes the definition proposed by \cite {Axe1}. Based on this, we propose a new class of complex nonsymmetric…
Quasi-Newton methods form an important class of methods for solving nonlinear optimization problems. In such methods, first order information is used to approximate the second derivative. The aim is to mimic the fast convergence that can be…
Motivated by Ridgway's proof of the perceptron algorithm, we study a simple subgradient method for convex inequality systems in Hilbert space. Assuming strict feasibility and bounded subgradients, we establish finite termination for several…
The DANE algorithm is an approximate Newton method popularly used for communication-efficient distributed machine learning. Reasons for the interest in DANE include scalability and versatility. Convergence of DANE, however, can be tricky;…
Semismooth* Newton methods have been proposed in recent years targeting multi-valued inclusion problems and have been successfully implemented to deal with several concrete generalized equations. In this paper, we show that two typical…
In this paper, applying the Newton method, we transform the complex continuous-time algebraic Riccati matrix equation into a Lyapunov equation. Then, we introduce an efficient general alternating-direction implicit (GADI) method to solve…
We investigate a globalized inexact semismooth Newton method applied to strongly convex optimization problems in Hilbert spaces. Here, the semismooth Newton method is appplied to the dual problem, which has a continuously differentiable…
Inverse eigenvalue and singular value problems have been widely discussed for decades. The well-known result is the Weyl-Horn condition, which presents the relations between the eigenvalues and singular values of an arbitrary matrix. This…
A general formula is presented for any order derivative of Chebyshev polynomials instead of the existing recursive relationship. Hence, the Chebyshev finite difference method is made applicable not only to second order problems but also to…
In this paper we investigate adaptive discretization of the iteratively regularized Gauss- Newton method IRGNM. All-at-once formulations considering the PDE and the measurement equation simultaneously allow to avoid (approximate) solution…
We establish a general principle which states that regularizing an inverse problem with a convex function yields solutions which are convex combinations of a small number of atoms. These atoms are identified with the extreme points and…
In two and three dimensions, we analyze a finite element method to approximate the solutions of an eigenvalue problem arising from neutron transport. We derive the eigenvalue problem of interest, which results to be non-symmetric. Under a…
This paper provides an overview of the necessary and sufficient conditions for guaranteeing the unique solvability of absolute value equations. In addition to discussing the basic form of these equations, we also address several…
We propose new iterative methods for computing nontrivial extremal generalized singular values and vectors. The first method is a generalized Davidson-type algorithm and the second method employs a multidirectional subspace expansion…
Solutions to conservation laws satisfy the monotonicity property: the number of local extrema is a non-increasing function of time, and local maximum/minimum values decrease/increase monotonically in time. This paper investigates this…
Finding roots of equations is at the heart of most computational science. A well-known and widely used iterative algorithm is the Newton's method. However, its convergence depends heavily on the initial guess, with poor choices often…
Let $A$ be a real $n\times n$ matrix and $z,b\in \mathbb R^n$. The piecewise linear equation system $z-A\vert z\vert = b$ is called an absolute value equation. It is equivalent to the general linear complementarity problem, and thus NP hard…