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ABOUT ALGORITHM FOR THE TRIANGULAR DECOMPOSITION IN A COMMUTATIVE RING

Annotation

We give a description of a block-recursive algorithm for the triangular matrix decomposition which has a complexity of matrix multiplication. The algorithm is illustrated by numerical examples in which we find the decomposition of an integer matrix. The algorithm is effective for computer systems with distributed memory.

Keywords

triangular decomposition; integral domain; matrix decomposition

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UDC

512.7

Pages

1293-1302

References

1. Malaschonok G.I. Effective matrix methods in commutative domains. In: D. Krob, A.A. Mikhalev, A.V. Mikhalev (eds.) Formal Power Series and Algebraic Combinatorics, Springer, Berlin, 2000. P. 506–517. 2. Malaschonok G.I. A fast algorithm for adjoint matrix computation // Tambov University Reports. 2000. V. 5. № 1. P. 142-146. 3. Malaschonok G.I. Matrix Computational Methods in Commutative Rings. Tambov: Tambov University Publishing House, 2002. 4. Malaschonok G.I. Fast matrix decomposition in parallel computer algebra // Tambov University Reports. 2010. V. 15. № 4. P. 1372-1385. 5. Malaschonok G.I. Fast generalized Bruhat decomposition. In: Ganzha, V.M., Mayr, E.W., Vorozhtsov, E.V. (eds.) 12th International Workshop on Computer Algebra in Scientific Computing. LNCS 6244. Springer, Berlin, Heidelberg, 2010. P. 194-202. 6. Malaschonok G.I. On the fast generalized Bruhat decomposition in domains // Tambov University Reports. 2012. V. 17. № 2. P. 544-550. 7. Malaschonok G.I. Fast generalized Bruhat decomposition. In: 15th International Workshop on Computer Algebra in Scientific Computing. LNCS 6244. Springer, Berlin, Heidelberg, 2013. P. 194-202. 8. Malaschonok G.I., Scherbinin A.S. Triangular Decomposition of Matrices in a Domain. In: 17th International Workshop on Computer Algebra in Scientific Computing. Springer, Berlin, Heidelberg, 2015. (in print).

Received

2015-06-11

Section of issue

Scientific articles

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