Numerical solution of algebraic equations with roots of almost equal absolute value

Numerical Solution of Algebraic Riccati Equations

Society for induStrial and applied MatheMaticS Numerical Solution of Algebraic Riccati Equations Dario A. Bini, Bruno Iannazzo, and Beatrice Meini Fundamentals of Algorithms 9 This concise and comprehensive treatment of the basic theory of algebraic Riccati equations describes the classical as well as the more advanced algorithms for their solution in a manner that is accessible to both practit...

Numerical Solution of Differential Algebraic Equations

Numerical Solution of Projected Algebraic Riccati Equations

We consider the numerical solution of projected algebraic Riccati equations using Newton’s method. Such equations arise, for instance, in model reduction of descriptor systems based on positive real and bounded real balanced truncation. We also discuss the computation of low-rank Cholesky factors of the solutions of projected Riccati equations. Numerical examples are given that demonstrate the ...

Numerical solution of non-linear algebraic equations with discontinuities

The solution of systems of non-linear algebraic equations with discontinuities in the solution search domain is considered. It is demonstrated that such problems are often very difficult to solve, even with the state of the art numerical solvers, and even when initial guesses close to the solutions are used. The application of constrained solution methods that do not require evaluation of funct...

Numerical solution of Voltra algebraic integral equations by Taylor expansion method

Algebraic integral equations is a special category of Volterra integral equations system,  that has many applications in physics and engineering. The principal aim of this paper is to serve the numerical solution of an integral algebraic equation by using the Taylor expansion method. In this method, using the Taylor expansion of the unknown function, the algebraic integral equation system becom...