The independent variable technique for sparse linear equations

A novel algorithm is presented for solving large systems of sparse linear equations. The solution of these equations is based upon the selection of one or more independent variable(s), and the values of all other variables are expressed in terms of them during the solution process. Optimal order is applied through minimizing the number of independent variables, which in effect reduces the number of ill-ins. Hence, both round-off error and storage are minimized. The algorithm also takes numerical stability into consideration. It is shown how the algorithm can be used to find the solution in terms of designable entries in the system matrix. Examples are given to illustrate the storage and algorithm. A comparison with other techniques for both number of fill-ins and computational effort is also given. There is a significant saving in computation effort, and the housekeeping in the independent variable technique is minimal in comparison with other techniques