The ADI Model Problem

The ADI Model Problem presents the theoretical foundations of Alternating Direction Implicit (ADI) iteration for systems with both real and complex spectra, and extends early work for real spectra into the complex plane with methods for computing optimum iteration parameters for both one and two variable problems. This book applies theory to the solution of boundary value problems and describes the stable similarity reduction of a full matrix to low-band upper Hessenberg form, with application to computation of eigenvalues and solution of Lyapunov and Sylvester equations. 

This book includes MATLAB programs and numerical verification of theory and applications.