Some iterative methods for the solution of a symmetric indefinite KKT system

Preconditioners for Karush–Kuhn–Tucker Systems arising in Optimal Control

Mathematics (ABSTRACT) This work is concerned with the construction of preconditioners for indefinite linear systems. The systems under investigation arise in the numerical solution of quadratic programming problems, for example in the form of Karush–Kuhn–Tucker (KKT) optimality conditions or in interior–point methods. Therefore, the system matrix is referred to as a KKT matrix. It is not the p...

Preconditioning Indefinite Systems in Interior-Point Methods for quadratic optimization

A new class of preconditioners is proposed for the iterative solution of symmetric indefinite systems arising from interior-point methods. The use of logarithmic barriers in interior point methods causes unavoidable ill-conditioning of linear systems and, hence, iterative methods fail to provide sufficient accuracy unless appropriately preconditioned. Now we introduce two types of preconditione...

Iterative Method for Mirror-Symmetric Solution of Matrix Equation AXB + CY D = E

Preconditioned Generalized Minimal Residual Method for Solving Fractional Advection-Diffusion Equation

Introduction Fractional differential equations (FDEs)  have  attracted much attention and have been widely used in the fields of finance, physics, image processing, and biology, etc. It is not always possible to find an analytical solution for such equations. The approximate solution or numerical scheme  may be a good approach, particularly, the schemes in numerical linear algebra for solving ...

A new iteration method for solving a class of Hammerstein type integral equations system

In this work, a new iterative method is proposed for obtaining the approximate solution of a class of Hammerstein type Integral Equations System. The main structure of this method is based on the Richardson iterative method for solving an algebraic linear system of equations. Some conditions for existence and unique solution of this type equations are imposed. Convergence analysis and error bou...