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Bareiss Algorithm
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 of any round-off errors beyond those already present in the input. Overview Determinant definition has only multiplication, addition and subtraction operations. Obviously the determinant is integer if all matrix entries are integer. However actual computation of the determinant using the definition or Leibniz formula is impractical, as it requires O(''n!'') operations. Gaussian elimination has O(''n''3) complexity, but introduces division, which results in round-off errors when implemented using floating point numbers. Round-off errors can be avoided if all the numbers are k ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erwin Bareiss
Erwin may refer to: People Given name * Erwin Chargaff (1905–2002), Austrian biochemist * Erwin Chemerinsky (born 1953), American legal scholar * Erwin Dold (1919–2012), German concentration camp commandant in World War 2 * Erwin Hauer (1926–2017), Austrian-born American sculptor * Egon Erwin Kisch (1885–1948), Czechoslovak writer and journalist * Erwin Emata (born 1973), Filipino mountain climber * Erwin James (born 1957), British writer and journalist * Erwin Josi (born 1955), Swiss alpine skier * Erwin Klein (died 1992), American table tennis player * Erwin Koeman (born 1961), Dutch footballer and coach * Erwin Kramer (1902–1979), East German politician * Erwin Kreyszig (1922–2008), American academic * Erwin Neutzsky-Wulff (born 1949), Danish author and philosopher * Erwin Osen (1891–1970), Austrian painter and mime artist * Erwin Panofsky (1892-1968), German-Jewish art historian * Erwin Ramírez (born 1971), Ecuadorian football player * Erwin Rommel (1891– ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |