2006 | OriginalPaper | Chapter
Computation of the Adjoint Matrix
Authors : Alkiviadis Akritas, Gennadi Malaschonok
Published in: Computational Science – ICCS 2006
Publisher: Springer Berlin Heidelberg
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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
log
n
log log
n
) operations, provided that the complexity of the algorithm for multiplying two matrices is
γn
β
+
o
(
n
β
). For a commutative domain – and under the same assumptions – the complexity of the best method is 6
γn
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.