Iterative solution of rectangular systems of linear algebraic equations

Solution of Systems of Linear Algebraic Equations

Iterative Solution of Linear Systems

Recent advances in the eld of iterative methods for solving large linear systems are reviewed. The main focus is on developments in the area of conjugate gradient-type algorithms and Krylov subspace methods for non-Hermitian matrices .

‎Finite iterative methods for solving systems of linear matrix equations over reflexive and anti-reflexive matrices

A matrix $Pintextmd{C}^{ntimes n}$ is called a generalized reflection matrix if $P^{H}=P$ and $P^{2}=I$‎. ‎An $ntimes n$‎ ‎complex matrix $A$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $P$ if $A=PAP$ ($A=-PAP$)‎. ‎In this paper‎, ‎we introduce two iterative methods for solving the pair of matrix equations $AXB=C$ and $DXE=F$ over reflexiv...

An Optimal Linear Estimation Approach to the Parallel Solution of Linear Algebraic Systems of Equations

Resumo Estimação linear ótima estocástica de parâmetros é utilizada para gerar um novo método iterativo, para a solução paralela de sistemas algébricos de equações. No limite, a abordagem proposta leva a algoritmos iterativos que resolvem em paralelo sistemas lineares, variável por variável. É mostrado, tanto no caso de sistemas determinados como no de sistemas indeterminados, que o método iter...

Iterative Solution of Piecewise Linear Systems

Abstract. The correct formulation of numerical models for free-surface hydrodynamics often requires the solution of special linear systems whose coefficient matrix is a piecewise constant function of the solution itself. In so doing one may prevent the development of unrealistic negative water depths. The resulting piecewise linear systems are equivalent to particular linear complementarity pro...