A comparison of iterative methods for solving nonsymmetric linear systems

Iterative methods, which were initially developed for the solution of symmetric linear systems, have more recently been extended to the nonsymmetric case. Nonsymmetric linear systems arise in many applications, including the solution of elliptic partial differential equations. In this work, we provide a brief description of and discuss the relationship between five commonly used iterative techniques: CGNR, GMRES, BiCG, CGS and BiCGSTAB. We highlight the relative merits and deficiencies of each technique through the implementation of each in the numerical solution of several differential equations test problems. Preconditioning is used in each case. We also discuss the mathematical equivalence between a nonsymmetric Lanczos orthogonalization, and BiCG.