Cholesky Decomposition

Given a symmetric Positive Definite Matrix ${\hbox{\sf A}}$, the Cholesky decomposition is an upper Triangular Matrix ${\hbox{\sf U}}$ such that

$${\hbox{\sf A}} = {\hbox{\sf U}}^{\rm T}{\hbox{\sf U}}.$$

See also LU Decomposition, QR Decomposition

References

Nash, J. C. ``The Choleski Decomposition.'' Ch. 7 in Compact Numerical Methods for Computers: Linear Algebra and Function Minimisation, 2nd ed. Bristol, England: Adam Hilger, pp. 84-93, 1990.

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Cholesky Decomposition.'' §2.9 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 89-91, 1992.