Robust Approximate Cholesky Factorization of Rank-Structured Symmetric Positive Definite Matrices
SIAM Journal on Matrix Analysis and Applications
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As one of the basic problems in matrix computation, rank-revealing arises in a wide variety of applications in scientific computing. Although the singular value decomposition is the standard rank-revealing method, it is costly in both computing time and storage when the rank or the nullity is low, and it is inefficient in updating and downdating when rows and columns are inserted or deleted. Consequently, alternative methods are in demand in those situations. Following up on a recent rank-revealing algorithm by Li and Zeng for the low nullity case, we present a new rank-revealing algorithm for low rank matrices with efficient and straightforward updating/downdating capabilities. The method has been implemented in Matlab, and the numerical results show that the new algorithm appears to be efficient and robust.