Computation of the adjoint matrix

Abstract

The best method for computing the adjoint matrix of an order n matrix in an arbitrary commutative ring requires O(nβ+1/3 log n log log n) operations, provided that the complexity of the algorithm for multiplying two matrices is γnβ + o(nβ). For a commutative domain - and under the same assumptions - the complexity of the best method is 6γnβ(2β - 2) + o(nβ). 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. © Springer-Verlag Berlin Heidelberg 2006.