Related papers: Iterative methods for linear systems of equations:…
Since most inverse problems arising in scientific and engineering applications are ill-posed, prior information about the solution space is incorporated, typically through regularization, to establish a well-posed problem with a unique…
Various approaches to iterative refinement (IR) for least-squares problems have been proposed in the literature and it may not be clear which approach is suitable for a given problem. We consider three approaches to IR for least-squares…
In this note we develop a numerical method for partial differential equations with changing type. Our method is based on a unified solution theory found by Rainer Picard for several linear equations from mathematical physics. Parallel to…
We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the…
This study investigates the effectiveness of Genetic Algorithms (GAs) in solving both linear and nonlinear systems of equations, comparing their performance to traditional methods such as Gaussian Elimination, Newton's Method, and…
It is well known that the choice of the iterative method is crucial in determining the speed of the converged solution. This article presents a detailed comparison between several iterative techniques for solving incmopressible…
We propose a protocol for solving systems of linear algebraic equations via quantum mechanical methods using the minimal number of qubits. We show that $(M+1)$-qubit system is enough to solve a system of $M$ equations for one of the…
The Kaczmarz method is a way to iteratively solve a linear system of equations $Ax = b$. One interprets the solution $x$ as the point where hyperplanes intersect and then iteratively projects an approximate solution onto these hyperplanes…
We present a new class of iterative schemes for solving initial value problems (IVP) based on discontinuous Galerkin (DG) methods. Starting from the weak DG formulation of an IVP, we derive a new iterative method based on a preconditioned…
Aussel et al. (J Optim Theory Appl 170 818-837 2016) introduced the concept of projected solutions for the quasi-variational inequalities with a non-self constraint map, that is, the case where the constraint map may take values outside the…
We present an acceleration method for sequences of large-scale linear systems, such as the ones arising from the numerical solution of time-dependent partial differential equations coupled with algebraic constraints. We discuss different…
Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear systems of equations with an exponential speedup. Here, we demonstrate a method for solving a particular system of equations by using the concept…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
The efficient solution of large-scale multiterm linear matrix equations is a challenging task in numerical linear algebra, and it is a largely open problem. We propose a new iterative scheme for symmetric and positive definite operators,…
Numerous scientific and engineering applications require numerically solving systems of equations. Classically solving a general set of polynomial equations requires iterative solvers, while linear equations may be solved either by direct…
In this paper, we study the problem of multipath channel estimation for direct sequence spread spectrum signals. To resolve multipath components arriving within a short interval, we propose a new algorithm called the least-squares based…
Since numbers in the computer are represented with a fixed number of bits, loss of accuracy during calculation is unavoidable. At high precision where more bits (e.g. 64) are allocated to each number, round-off errors are typically small.…
We present an auxiliary space theory that provides a unified framework for analyzing various iterative methods for solving linear systems that may be semidefinite. By interpreting a given iterative method for the original system as an…
The Kaczmarz algorithm is an iterative method for solving systems of linear equations. We introduce a modified Kaczmarz algorithm for solving systems of linear equations in a distributed environment, i.e. the equations within the system are…
The delay Lyapunov equation is an important matrix boundary-value problem which arises as an analogue of the Lyapunov equation in the study of time-delay systems $\dot{x}(t) = A_0x(t)+A_1x(t-\tau)+B_0u(t)$. We propose a new algorithm for…