Systems of linear algebraic equations Ax = b occur very often when large-scale mathematical models are treated. The solution of these systems is as a rule the most time-consuming part of the computational work when large-scale mathematical models are handled on computers. Therefore, it is important to be able to solve such problems efficiently. It is assumed that the systems Ax = b , which must be solved many times during the treatment of the models, are (i) very large (containing more than 10~6 equations) and (ii) general sparse. Moreover, it is also assumed that parallel computers with shared memory are available. An efficient algorithm for the solution of such large systems under the above assumptions is described. Numerical examples are given to demonstrate the ability of the algorithm to handle very large systems of linear algebraic equations. The algorithm can be applied in the treatment of some large-scale air pollution models without using splitting procedures.
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