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Some new rigorous perturbation bounds for the generalized Cholesky factorization with normwise or componentwise perturbations in the given matrix are obtained, where the componentwise perturbation has the form of backward rounding error for the generalized Cholesky factorization algorithm. These bounds can be much tighter than some existing ones while the conditions for them to hold are simple and moderate.
We introduce a randomized algorithm, namely RCHOL, to construct an approximate Cholesky factorization for a given Laplacian matrix (a.k.a., graph Laplacian). From a graph perspective, the exact Cholesky factorization introduces a clique in the underl
We propose to compute a sparse approximate inverse Cholesky factor $L$ of a dense covariance matrix $Theta$ by minimizing the Kullback-Leibler divergence between the Gaussian distributions $mathcal{N}(0, Theta)$ and $mathcal{N}(0, L^{-top} L^{-1})$,
We present rigorous performance bounds for the optimal dynamical decoupling pulse sequence protecting a quantum bit (qubit) against pure dephasing. Our bounds apply under the assumption of instantaneous pulses and of bounded perturbing environment an
We prove that every positive semidefinite matrix over the natural numbers that is eventually 0 in each row and column can be factored as the product of an upper triangular matrix times a lower triangular matrix. We also extend some known results abou
We introduce a task-parallel algorithm for sparse incomplete Cholesky factorization that utilizes a 2D sparse partitioned-block layout of a matrix. Our factorization algorithm follows the idea of algorithms-by-blocks by using the block layout. The al