Relation between the cholesky upper triangular matrix of $A$ and the one of $A^{-1}$

Question

Let $A$ be a symmetric, positive definite, real matrix (in short "spd matrix") and let $chol(A)$ be the upper triangular matrix obtained from $A$ by Cholesky decomposition. Is there any relation between $chol(A)$ and $chol(A^{-1})$ that allows to transform the former into the latter (and/or viceversa)?

Clearly the relation $chol(A^{-1})$=$(chol(A))^{-1}$ does not hold. Is there any other known relation?

Thanks!