![]() ![]() We also exploit the sparsity of the matrices and vectors to accelerate the overall computation. We provide two algorithms-a direct method and a hybrid direct-iterative method-for solving the augmented system. Our algorithms augment the matrix to account for the changes in it, and then compute the solution to the augmented system without refactoring the modified matrix. This problem arises in the dynamic security analysis of a power grid, where operators need to perform $N-k$ contingency analysis, i.e., determine the state of the system when exactly $k$ links from $N$ fail. ![]() We present AMPS, an augmented matrix approach to update the solution to a linear system of equations when the matrix is modified by a few elements within a principal submatrix. ![]()
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