Computation of the Adjoint Matrix
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The best method for computing the adjoint matrix of an order n matrix in an arbitrary commutative ring requires O(n^β+1/3 n n) operations, provided the complexity of the algorithm for multiplying two matrices is γ n^β+o(n^β). For a commutative domain -- and under the same assumptions -- the complexity of the best method is 6γ n^β/(2^β-2)+o(n^β). In the present work a new method is presented for the computation of the adjoint matrix in a commutative domain. Despite the fact that the number of operations required is now 1.5 times more, than that of the best method, this new method permits a better parallelization of the computational process and may be successfully employed for computations in parallel computational systems.
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