ON THE GENERAL-SOLUTION BY A DIRECT METHOD OF A LARGE-SCALE SINGULAR SYSTEM OF LINEAR-EQUATIONS - APPLICATION TO THE ANALYSIS OF FLOATING STRUCTURES

Finding the general solution of a singular system of linear equations requires computing a particular solution and a basis of the null space of the corresponding singular matrix. In this paper, we consider the case where the singular matrix is large and sparse, and the applicatio n calls for a direct solution method. We highlight the dependence of s traight forward factorization algorithms on an arbitrary constant that can influence the correctness of the computed solution, and describe a family of improved direct solution methods that alleviate this probl em. For structural mechanics applications, we propose a hybrid geometr ic-algebraic method that is more robust than the purely algebraic dire ct methods that are currently used for solving singular sparse systems of equations. We illustrate the potential of our proposed solution al gorithms with examples from structural mechanics and domain-decomposit ion-based iterative solvers. (C) 1998 John Wiley & Sons, Ltd.