Abstract
This chapter discusses the adapting iterative algorithms developed for symmetric systems to nonsymmetric systems. The iterative algorithms utilized in the ITPACK computer package for solving large sparse linear systems of equations assume that the coefficient matrix is symmetric positive definite. The mumerical solutions of boundary-value problems with self-adjoint partial differential equations may result in symmetric systems when low order discretizations are used and however, the use of higher-order discretizations may result in nonsymmetric systems that are nearly symmetric. Non-self-adjoint equations or mixed boundary conditions may result in nonsymmetric systems. The chapter presents the formulas for conjugate gradient acceleration that are used in ITPACK 2.0 and the modified formulas that are used in ITPACK 2A. It is interesting to observe that for both modified schemes, the Jacobi matrix B for the natural ordering tends to a zero matrix with nonzero constants on the superdiagonal. The spectral radius of B approaches zero as β increases to infinity.
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