Efficient parallel solution of linear systems
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Designing efficient algorithms for parallel computers
Designing efficient algorithms for parallel computers
Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Matrix computations (3rd ed.)
Optimal Algorithms for Well-Conditioned Nonlinear Systems of Equations
IEEE Transactions on Computers
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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(n/sup 2/) operations, reducing the time for obtaining the solution of linear equations. The more lengthy calculation of the inverse itself, which requires O(n/sup 3/) 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.