Bareiss algorithm ^{en}
In mathematics, the Bareiss algorithm, named after Erwin Bareiss, is an algorithm to calculate the determinant or the echelon form of a matrix with integer entries using only integer arithmetic; any divisions that are performed are guaranteed to be exact. The method can also be used to compute the determinant of matrices with real entries, avoiding the introduction any roundoff errors beyond those already present in the input. During the execution of Bareiss algorithm, every integer that is computed is the determinant of a submatrix of the input matrix. This allows, using Hadamard inequality, to bound the size of these integers. Otherwise, Bareiss algorithm may be viewed as a variant of Gaussian elimination and needs roughly the same number of arithmetic operations. It follows that, for an n × n matrix of maximum value 2ᴸ for each entry, the Bareiss algorithm runs in O elementary operations with an O bound on the absolute value of intermediate values needed. Its computational complexity is thus O when using elementary arithmetic or O by using fast multiplication. [  ]
Freebase Commons Metaweb System Types /type
 
 Bareiss algorithm
 /en/bareiss_algorithm
 /wikipedia/uk_title/$041C$0435$0442$043E$0434_$041C$043E$043D$0442$0430$043D$0442$0435
 /wikipedia/pl_id/2326496
 /wikipedia/es_id/671647
 /wikipedia/es_title/M$00E9todo_Montante
 /wikipedia/es/M$00E9todo_Montante
 /wikipedia/en_id/17919686
 /wikipedia/uk/$041C$0435$0442$043E$0434_$041C$043E$043D$0442$0430$043D$0442$0435
 /wikipedia/en/Bareiss_algorithm
 /wikipedia/pl/Metoda_Montantego
 /wikipedia/en/Bareiss_Algorithm
 /wikipedia/pl_title/Algorytm_Bareissa
 /wikipedia/pl/Algorytm_Bareissa
 /wikipedia/es/Metodo_Montante
 /wikipedia/en_title/Bareiss_algorithm
 /wikipedia/uk_id/855142
 /wikipedia/en/Montante$0027s_method
 
 
 
 
 http://uk.wikipedia.org/wiki/Метод_Монтанте
 http://es.wikipedia.org/wiki/index.html?curid=671647
 http://es.wikipedia.org/wiki/Método_Montante
 http://en.wikipedia.org/wiki/index.html?curid=17919686
 http://es.wikipedia.org/wiki/M%C3%A9todo_Montante
 http://uk.wikipedia.org/wiki/%D0%9C%D0%B5%D1%82%D0%BE%D0%B4_%D0%9C%D0%BE%D0%BD%D1%82%D0%B0%D0%BD%D1%82%D0%B5
 http://pl.wikipedia.org/wiki/Algorytm_Bareissa
 http://uk.wikipedia.org/wiki/index.html?curid=855142
 http://en.wikipedia.org/wiki/Bareiss_algorithm
 http://pl.wikipedia.org/wiki/index.html?curid=2326496
 
 
 
 
 
 

 
 