Introduction

ITPACKV is a collection of seven FORTRAN subroutines for solving large sparse linear systems by adaptive accelerated iterative algorithms. Basic iterative procedures, such as the Jacobi method, the Successive Overrelaxation method, the Symmetric Successive Overrelaxation method, and the RS method for the reduced system are combined, where possible, with acceleration procedures, such as Chebyshev (Semi-Iteration) and Conjugate Gradient, for rapid convergence. Automatic selection of the acceleration parameters and the use of accurate stopping criteria are major features of this software package. While the ITPACKV routines can be called with any linear system containing positive diagonal elements, they are most successful in solving systems with symmetric positive definite or mildly nonsymmetric coefficient matrices.

ITPACKV 2D is an adaptation for vector computers of the linear equation solution algorithms in the ITPACK 2C software package. See reference [6] for more details on the scalar version. The data structure used to contain the coefficient matrix was changed to a format allowing greater efficiency on vector computers while being flexible enough to accommodate matrix problems with general structure. The data structure in the vector version was chosen to coincide with the ELLPACK [10] data structure, which can efficiently store matrices arising from discretizations of partial differential equations on general domains. Throughout this paper, we adopt notation such as SOR() when referring to a subroutine, U(*) when referring to a singly-dimensioned array, and COEF(*,*) for a doubly-dimensioned array. The residual vector is b-Au⁽ⁿ⁾ for the linear system Au=b and the pseudo-residual vector is Gu⁽ⁿ⁾+k-u⁽ⁿ⁾ for a basic iterative method of the form u⁽ⁿ⁺¹⁾=Gu⁽ⁿ⁾+k. The smallest and largest eigenvalues of the iteration matrix G are denoted m(G) and M(G), respectively.