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Linear programming (LP) is a fundamental optimization problem with broad applications across science, engineering, and business. One of the most widely used algorithms for solving LPs is interior point methods (IPM), which are known to converge fast both...

We present a new LDL factorization algorithm that requires O(nt^{omega-1}) field operations, where t is the treewidth of the graph associated with the nonzeros of a full-rank sparse matrix. This algorithm matches the best known bounds for Cholesky and...