In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced /ʃəˈlɛski/shə-LES-kee) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations. It was discovered by André-Louis Cholesky for real matrices, and posthumously published in 1924.[1]
When it is applicable, the Cholesky decomposition is roughly twice as efficient as the LU decomposition for solving systems of linear equations.[2]
^Benoit (1924). "Note sur une méthode de résolution des équations normales provenant de l'application de la méthode des moindres carrés à un système d'équations linéaires en nombre inférieur à celui des inconnues (Procédé du Commandant Cholesky)". Bulletin Géodésique (in French). 2: 66–67. doi:10.1007/BF03031308.
^Press, William H.; Saul A. Teukolsky; William T. Vetterling; Brian P. Flannery (1992). Numerical Recipes in C: The Art of Scientific Computing (second ed.). Cambridge University England EPress. p. 994. ISBN 0-521-43108-5. Retrieved 2009-01-28.
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