Abstract
The object of this paper is to introduce a new and fascinating method of solving large linear equations, based on Cramer's rule or Gaussian elimination but employing Sylvester's determinant identity in its computation process. In addition, a scheme suitable for parallel computing is presented for this kind of generalized Chiò's determinant condensation processes, which makes this new method have a property of natural parallelism. Finally, some numerical experiments also confirm our theoretical analysis.
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