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$A$ is symmetric positive definite matrix and $S$ is such that $A=SS^{T}$. Further $y=Sz$ Does there exist a simple ( or any verifiable) relation exist only involving $A$,$y$ and $z$ ? Thanks

I have SPD matrix A and two vectors z and b. Is there exist a norm where I can calculate $||A^{1/2}b-z||$ without having to calculate $A^{1/2}b$ explicitly ?

What is a good way to check if the any numerical error is occured in conjugate gradient algorithm. Additionally why is it not suggested to check error by checking A-orthogonality of search direction o …

I have a symmetric positive definite (SPD) matrix $A$ that needs to be factorized as ${A=SS^{T}}$. However, using the Cholesky decomposition for this purpose is prohibitive in terms of computational c …

I am interested in cases where Conjugate gradient works much better than GMRES method. In general, CG is preferable choice in many cases of SPD because it requires less storage and theoretical bound …

I am multiplying a matrix $A$ with vector $p$. However, the matrix $A$ isn't accurate. Some (a very small fraction) of the element's value is changed from $a_{i,j}$ to {0,$-a_{i,j}$, $2a_{i,j}$}. Ho …