Approximate Solution of Large Linear Algebraic Systems Using Differential Equations

摘要

Vector differential equations are constructed and then integrated numerically over an interval extended from a convenient starting value of the unknown to a value which gives the solution of the system of equations. The solution procedure allows to easily control and monitor the magnitude of the residual vector of the algebraic system at each step of the integration process. The method is flexible, permitting various intervening parameters to be changed wherever necessary in order to increase its efficiency. A smaller amount of computation is needed to obtain an approximate solution of very large linear systems as compared to existing methods. An electrostatic field model is suggested which could be useful for investigating techniques to further improve the efficiency of the proposed method.