Let a Matrix $\mathbf{Y=[A\;b;b^T\;}d]$, where $d$ is a scalar, and $\mathbf{b}$ is a vector. How to find the cholesky factorization of $\mathbf{Y}$ if i know the cholesky factorization of $\mathbf{A}$.?

  • 3
    $\begingroup$ Welcome to SciComp.SE! This is called an update of the Cholesky factorization; you can find a discussion in many textbooks and papers as well as at math.stackexchange.com/questions/955874/…. $\endgroup$ Oct 21, 2015 at 7:52
  • $\begingroup$ @ChristianClason Thanks for the link. Additionally can we update the cholesky factorization of A1=[A a] after a column addition? $\endgroup$
    – Astro
    Oct 21, 2015 at 8:34
  • $\begingroup$ No, because the matrix $A1$ needs to be symmetric and positive definite for a Cholesky factorization to exist, and adding a column without adding a row leads to a non-square matrix which can't be symmetric. $\endgroup$ Oct 21, 2015 at 8:38
  • $\begingroup$ @ChristianClason Oh! My bad. sorry i intended to ask something else. Anyway i got the answer from the link you sent. $\endgroup$
    – Astro
    Oct 21, 2015 at 8:44


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.