Low Rank Updates for the Cholesky Decomposition

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Bayesian Posterior Sampling via Stochastic Gradient Fisher Scoring (2012, neutral): “A more numerically stable alternative is to update Cholesky factors (Seeger, 2004).”
Building Support Vector Machines with Reduced Classifier Complexity (2006, methodology): “Even with J fixed, during the course of solving (4) via the Newton method, P will undergo changes due to changes in I. Efficient rank one schemes can be used to do the updating of the Cholesky factorization (Seeger, 2004).”
Semiparametric latent factor models (2005, methodology): “An algorithm for chollrup can be found in [8] or [9].”
Laplacian Support Vector Machines Trained in the Primal (2009, methodology): “In order to reduce the cost of each iteration, a Cholesky factorization of the Hessian can be computed before performing the first matrix inversion, and it can be updated using a rank–1 scheme during the following iterations, with cost O(n2) for each update (Seeger, 2008).”
Gaussian Process Structural Equation Models with Latent Variables (2010, methodology): “Fast submatrix updates of K − 1 i ; M and K i ; NM K − 1 i ; M are required in order to calculate l i ( · ) at a O ( NM ) cost, which can be done by standard Cholesky updates (Seeger, 2004).”
Gaussian Kullback-Leibler approximate inference (2013, methodology): “Efficient exact implementations of this method maintain the covariance using its Cholesky factorisation and perform efficient rank one Cholesky updates (Seeger, 2007).”