Methods for modifying matrix factorizations

By Gene H. Golub, Philip E. Gill, Walter Murray, Michael A. Saunders. 1972

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Citations in the corpus

• Incremental smoothing and mapping (2008, methodology): “Golub and Van Loan [60] present general methods for updating matrix factorizations based on [59, 58], including the Givens rotations I use in this work.”
• Online Kernel Principal Component Analysis: A Reduced-Order Model (2012, methodology): “To address this drawback, different incremental techniques have been proposed, such as [2], [3], or more recently [4] (and references therein), however still with high computational cost.”
• Factor Graphs for Robot Perception (2017, methodology): “Golub and Van Loan [84] present general methods for updating matrix factorizations based on [83, 77], including the Givens rotations we use in this work.”
• iSAM2: Incremental smoothing and mapping using the Bayes tree (2012, methodology): “New measurements are added using matrix update equations (Gill et al., 1974; Gentleman, 1973; Golub and Loan, 1996), so that previously calculated components of the square root information matrix are reused.”
• qpOASES: a parametric active-set algorithm for quadratic programming (2014, methodology): “This technique is central to the efficiency of active-set methods and goes back to [4,25].”
• Historical development of the BFGS secant method and its characterization properties (2009, methodology): “Methods that utilized this idea originated in the work of Gill and Murray [57] in 1972, and were subsequently developed and analyzed by Goldfarb [60] and Gill, Golub, Murray, Saunders [56], among others.”
• A Class of Parallel Tiled Linear Algebra Algorithms for Multicore Architectures (2007, unknown): “[24].”
• Fast Gaussian process methods for point process intensity estimation (2008, background): “This decomposition can be seen as a partial rank-one (blockwise) update to a Cholesky factorization (Gill et al., 1974), in that D can triv­ially be factorized to D 21 .”
• iSAM: Incremental Smoothing and Mapping (2008, methodology): “Golub and Van Loan [8] present general methods for updating matrix factorizations based on [53], [54], including the Givens rotations we use in this paper.”