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 $\mathbf{A}$.?
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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/…. $\endgroup$– Christian ClasonOct 21, 2015 at 7:52
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$\begingroup$ @ChristianClason Thanks for the link. Additionally can we update the cholesky factorization of A1=[A a] after a column addition? $\endgroup$– AstroOct 21, 2015 at 8:34
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$\begingroup$ 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. $\endgroup$– Christian ClasonOct 21, 2015 at 8:38
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$\begingroup$ @ChristianClason Oh! My bad. sorry i intended to ask something else. Anyway i got the answer from the link you sent. $\endgroup$– AstroOct 21, 2015 at 8:44
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