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 $O(n^{\beta +1/3}\log n\log \log n)$ operations, provided the complexity of the algorithm for multiplying two matrices is $\gamma n^{\beta }+o(n^{\beta })$. For a commutative domain -- and under the same assumptions -- the complexity of the best method is $6\gamma n^{\beta }/(2^{\beta }-2)+o(n^{\beta })$. 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.

Cited by in corpus (1)

• Fast generalized Bruhat decomposition