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- Bareiss_algorithm abstract "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 (there is no remainder). The method can also be used to compute the determinant of matrices with (approximated) real entries, avoiding the introduction any round-off 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 (absolute) value 2L for each entry, the Bareiss algorithm runs in O(n3) elementary operations with an O(n n/2 2nL) bound on the absolute value of intermediate values needed. Its computational complexity is thus O(n5L2 (log(n)2 + L2)) when using elementary arithmetic or O(n4L (log(n) + L) log(log(n) + L))) by using fast multiplication.The general Bareiss algorithm is distinct from the Bareiss algorithm for Toeplitz matrices.".
- Bareiss_algorithm wikiPageID "17919686".
- Bareiss_algorithm wikiPageLength "2261".
- Bareiss_algorithm wikiPageOutDegree "20".
- Bareiss_algorithm wikiPageRevisionID "662062086".
- Bareiss_algorithm wikiPageWikiLink Algorithm.
- Bareiss_algorithm wikiPageWikiLink Analysis_of_algorithms.
- Bareiss_algorithm wikiPageWikiLink Big_O_notation.
- Bareiss_algorithm wikiPageWikiLink Category:Computer_algebra.
- Bareiss_algorithm wikiPageWikiLink Category:Determinants.
- Bareiss_algorithm wikiPageWikiLink Category:Exchange_algorithms.
- Bareiss_algorithm wikiPageWikiLink Category:Numerical_linear_algebra.
- Bareiss_algorithm wikiPageWikiLink Determinant.
- Bareiss_algorithm wikiPageWikiLink Division_(mathematics).
- Bareiss_algorithm wikiPageWikiLink Echelon_form.
- Bareiss_algorithm wikiPageWikiLink Erwin_Bareiss.
- Bareiss_algorithm wikiPageWikiLink Fast_multiplication.
- Bareiss_algorithm wikiPageWikiLink Gaussian_elimination.
- Bareiss_algorithm wikiPageWikiLink Hadamard_inequality.
- Bareiss_algorithm wikiPageWikiLink Hadamards_inequality.
- Bareiss_algorithm wikiPageWikiLink Integer.
- Bareiss_algorithm wikiPageWikiLink Mathematics_of_Computation.
- Bareiss_algorithm wikiPageWikiLink Matrix_(mathematics).
- Bareiss_algorithm wikiPageWikiLink Multiplication_algorithm.
- Bareiss_algorithm wikiPageWikiLink Real_number.
- Bareiss_algorithm wikiPageWikiLink Remainder.
- Bareiss_algorithm wikiPageWikiLink Row_echelon_form.
- Bareiss_algorithm wikiPageWikiLink Toeplitz_matrix.
- Bareiss_algorithm wikiPageWikiLinkText "Bareiss algorithm".
- Bareiss_algorithm hasPhotoCollection Bareiss_algorithm.
- Bareiss_algorithm wikiPageUsesTemplate Template:Algorithm-stub.
- Bareiss_algorithm wikiPageUsesTemplate Template:Citation.
- Bareiss_algorithm wikiPageUsesTemplate Template:Numerical_linear_algebra.
- Bareiss_algorithm subject Category:Computer_algebra.
- Bareiss_algorithm subject Category:Determinants.
- Bareiss_algorithm subject Category:Exchange_algorithms.
- Bareiss_algorithm subject Category:Numerical_linear_algebra.
- Bareiss_algorithm hypernym Algorithm.
- Bareiss_algorithm type Software.
- Bareiss_algorithm type Algorithm.
- Bareiss_algorithm type Determinant.
- Bareiss_algorithm comment "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 (there is no remainder).".
- Bareiss_algorithm label "Bareiss algorithm".
- Bareiss_algorithm sameAs Método_Montante.
- Bareiss_algorithm sameAs Algorytm_Bareissa.
- Bareiss_algorithm sameAs m.047rvt_.
- Bareiss_algorithm sameAs Метод_Монтанте.
- Bareiss_algorithm sameAs Q4860404.
- Bareiss_algorithm sameAs Q4860404.
- Bareiss_algorithm wasDerivedFrom Bareiss_algorithm?oldid=662062086.
- Bareiss_algorithm isPrimaryTopicOf Bareiss_algorithm.