Cholesky Square Root of a Matrix

Returns the Cholesky square root of the non-singular, symmetric matrix X. The purpose is mainly to demonstrate the algorithm used by Kennedy & Gentle (1980).

Usage

cholesky(X, tol = sqrt (.Machine$double.eps))

Arguments

X

a square symmetric matrix

tol

tolerance for checking for 0 pivot

Value

the Cholesky square root of X

References

Kennedy W.J. Jr, Gentle J.E. (1980). Statistical Computing. Marcel Dekker.

See also

Author

John Fox

Examples

C <- matrix (c (1,2,3,2,5,6,3,6,10), 3, 3) # nonsingular, symmetric
C
#> [,1] [,2] [,3]
#> [1,] 1 2 3
#> [2,] 2 5 6
#> [3,] 3 6 10
cholesky(C)
#> [,1] [,2] [,3]
#> [1,] 1 0 0
#> [2,] 2 1 0
#> [3,] 3 0 1
cholesky(C) %*%  t (cholesky(C)) # check
#> [,1] [,2] [,3]
#> [1,] 1 2 3
#> [2,] 2 5 6
#> [3,] 3 6 10