Direct Solution and Storage of Large Sparse Linear Systems

Publisher Summary A general method of representing a physical system by a mathematical model is to choose a number of points, called nodes, within the system at which equations are set up describing that aspect of the system which is of interest. Direct methods lead to an exact solution in a finite number of steps if roundoff error is not present. Most direct methods are based on Gaussian elimination which produces a system of equations with a triangular coefficient matrix which can then be easily solved. Variants arise from the different methods of intermediate storage and utilization of special properties of certain matrices. A method used for storing a symmetric banded matrix is called diagonal storage. All the diagonals of the lower triangle which contain non-zero entries are stored in a rectangular array with n rows and a number of columns equal to the maximum B i (A)+1. The Cuthill–McKee algorithm results in a variable bandwidth store which cannot have re-entrant rows. It may be considered to be made up of overlapping triangles.