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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 wikiPageRevisionID "568334172".
- Bareiss_algorithm hasPhotoCollection Bareiss_algorithm.
- 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 type Abstraction100002137.
- Bareiss_algorithm type Act100030358.
- Bareiss_algorithm type Activity100407535.
- Bareiss_algorithm type Algorithm105847438.
- Bareiss_algorithm type Cognition100023271.
- Bareiss_algorithm type CognitiveFactor105686481.
- Bareiss_algorithm type Determinant105692419.
- Bareiss_algorithm type Determinants.
- Bareiss_algorithm type Event100029378.
- Bareiss_algorithm type ExchangeAlgorithms.
- Bareiss_algorithm type Procedure101023820.
- Bareiss_algorithm type PsychologicalFeature100023100.
- Bareiss_algorithm type Rule105846932.
- Bareiss_algorithm type YagoPermanentlyLocatedEntity.
- 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 "Algorytm Bareissa".
- Bareiss_algorithm label "Bareiss algorithm".
- Bareiss_algorithm label "Método Montante".
- Bareiss_algorithm sameAs Método_Montante.
- Bareiss_algorithm sameAs Algorytm_Bareissa.
- Bareiss_algorithm sameAs m.047rvt_.
- Bareiss_algorithm sameAs Q4860404.
- Bareiss_algorithm sameAs Q4860404.
- Bareiss_algorithm sameAs Bareiss_algorithm.
- Bareiss_algorithm wasDerivedFrom Bareiss_algorithm?oldid=568334172.
- Bareiss_algorithm isPrimaryTopicOf Bareiss_algorithm.