An overlaying technique for solving linear equations in real-time computing

A computer organization for solving a continuous stream of sets of linear equations A×b with relatively close consecutive parameters is described. The conditions of closeness enabling this technique are monitored during the computations. The cycles of the computational process are divided into two stages: finding a solution of a current set of linear equations by multiplying components of a polynomial approximation of the inverse matrix by a right-hand-side vector; and calculating this inverse matrix in order to arrange for an approximation of the next inverse matrix. The former procedure can be performed in O(n²) operations, reducing the time for obtaining the solution of linear equations. The more lengthy calculation of the inverse itself, which requires O(n³) operations, can overlay the preparation of the upcoming set of equations in the next cycle. The approach can be effectively utilized for organization of real-time computations