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• W3166334775 abstract "The interior-point method solves large linear programming problems in a few iterations. Each iteration requires computing the solution to one or more linear systems. This constitutes the most expensive step of the method and reducing the time to solve these linear systems is a way of improving the method’s performance. Iterative methods such as the preconditioned conjugate gradient method can be used to solve them. Incomplete Cholesky factorization can be used as a preconditioner to the problem. However, breakdowns may occur during incomplete factorizations and corrections on the diagonal may be required. This correction is accomplished by adding a positive number to diagonal elements of the linear system matrix and the factorization of the new matrix is restarted. In this work, we propose modifications to controlled Cholesky factorization to avoid or decrease the number of refactorizations of diagonally modified matrices. Computational results show that the proposed techniques can reduce the time needed for solving linear programming problems by the interior-point method." @default.
• W3166334775 created "2021-06-22" @default.
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• W3166334775 date "2021-05-28" @default.
• W3166334775 modified "2023-10-17" @default.
• W3166334775 title "Modified controlled Cholesky factorization for preconditioning linear systems from the interior-point method" @default.
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• W3166334775 doi "https://doi.org/10.1007/s40314-021-01544-0" @default.
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