Abstract
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 6γn β/(2β–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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© 2006 Springer-Verlag Berlin Heidelberg
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Akritas, A., Malaschonok, G. (2006). Computation of the Adjoint Matrix. In: Alexandrov, V.N., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science – ICCS 2006. ICCS 2006. Lecture Notes in Computer Science, vol 3992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11758525_65
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DOI: https://doi.org/10.1007/11758525_65
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34381-3
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