mchol {fastmatrix}

The modified Cholesky factorization

Description

Compute the Cholesky factorization of a real symmetric but not necessarily positive definite matrix.

Usage

mchol(x)

Arguments

x

a symmetric but not necessarily positive definite matrix to be factored.

Value

The lower triangular factor of modified Cholesky decomposition, i.e., the matrix \bold{L} such that \bold{X} + \bold{E} = \bold{LL}^T, where \bold{E} is a nonnegative diagonal matrix that is zero if \bold{X} es sufficiently positive definite.

References

Gill, P.E., Murray, W., Wright, M.H. (1981). Practical Optimization. Academic Press, London.

Nocedal, J., Wright, S.J. (1999). Numerical Optimization. Springer, New York.

See Also

chol, ldl

Examples

# a non-positive-definite matrix
a <- matrix(c(4,2,1,2,6,3,1,3,-.004), ncol = 3)
try(chol(a)) # fails
z <- mchol(a)
z # triangular factor

# modified 'a' matrix
tcrossprod(z)