Solving eigenvalue response matrix equations with nonlinear techniques

Solving nonlinear eigenvalue problems

Jacobi Operational Matrix Approach for Solving Systems of Linear and Nonlinear Integro-Differential Equations

‎‎‎‎‎‎‎‎‎‎‎‎‎This paper aims to construct a general formulation for the shifted Jacobi operational matrices of integration and product‎. ‎The main aim is to generalize the Jacobi integral and product operational matrices to the solving system of Fredholm and Volterra integro--differential equations‎ which appear in various fields of science such as physics and engineering. ‎The Operational matr...

Iterative Algorithm for Solving a System of Nonlinear Matrix Equations

We discuss the positive definite solutions for the system of nonlinear matrix equations X − A∗Y−nA I and Y − B∗X−mB I, where n, m are two positive integers. Some properties of solutions are studied, and the necessary and sufficient conditions for the existence of positive definite solutions are given. An iterative algorithm for obtaining positive definite solutions of the system is proposed. Mo...

Nonlinear Approximation and Adaptive Techniques for Solving Elliptic Operator Equations

This survey article is concerned with two basic approximation concepts and their interrelation with the numerical solution of elliptic operator equations, namely nonlinear and adaptive approximation. On one hand, for nonlinear approximation based on wavelet expansions the best possible approximation rate, which a function can have for a given number of degrees of freedom, is characterized in te...

Solving Linear Matrix Equations by Matrix Decompositions

In this paper, a system of linear matrix equations is considered. A new necessary and sufficient condition for the consistency of the equations is derived by means of the generalized singular-value decomposition, and the explicit representation of the general solution is provided. Keywords—Matrix equation, Generalized inverse, Generalized singular-value decomposition.