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This book presents the foundations of Alternating Direction Implicit iteration for systems with both real and complex spectra and extends work for real spectra into the complex plane with methods for computing optimum iteration parameters.

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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 provides application of theory to the solution of boundary value problems and description of 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. Also included are MATLAB programs and numerical verification of theory and applications.

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The Peaceman-Rachford Model Problem.- The Two-Variable ADI Problem.- Model Problems and Preconditioning.- Complex Spectra.- Lyapunov and Sylvester Matrix Equations.- MATLAB Implementation.

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