Rank 1 update can be achieved in Matlab with the built-in function cholupdate(). More details about the function can be found here:

http://www.mathworks.com.au/help/matlab/ref/cholupdate.html

In R, the recommended Matrix package has added a function updown() to handle rank 1 update. However, the documentation of that function is not easy to understand, and I find the example given is misleading. That prompted me to replicate the Matlab example with the updown() function. The resulting code snippet is shown below.

library(matrixcalc) A <- symmetric.pascal.matrix(4) R <- chol(A) x <- c(0, 0, 0, 1) A + x%*%t(x) library(Matrix) R <- Cholesky(Matrix(A, sparse=T)) x <- Matrix(x) R1.sparse <- updown('+', x, R) R1 <- as(R1.sparse, 'Matrix') x <- Matrix(c(0, 0, 0, 1/sqrt(2))) R1.sparse <- updown('-', x, R) R1 <- as(R1.sparse, 'Matrix')

Note that matrices have to be in the sparse representation to be used in the updown() function.