TR-2008008: Schur Aggregation for Linear Systems and Determinants
نویسندگان
چکیده
We apply our recent preconditioning techniques to the solution of linear systems of equations and computing determinants. We combine these techniques with the Sherman–Morrison–Woodbury formula, its new variations, aggregation, iterative refinement, and advanced algorithms that rapidly compute sums and products either error-free or with the desired high accuracy. Our theoretical and experimental study shows the power of this approach.
منابع مشابه
TR-2007022: The Schur Aggregation for Linear Systems and Determinants
According to our previous theoretical and experimental study, additive preconditioners can be readily computed for ill conditioned matrices, but it is not straightforward how such preconditioners can help us to facilitate the solution of linear systems of equations, computation of determinants, and other fundamental matrix computations. We develop some nontrivial techniques for this task. By ap...
متن کاملTR-2007023: The Schur Aggregation for Linear Systems and Determinants
According to our previous theoretical and experimental study, additive preconditioners can be readily computed for ill conditioned matrices, but it is not straightforward how such preconditioners can help us to facilitate the solution of linear systems of equations, computation of determinants, and other fundamental matrix computations. We develop some nontrivial techniques for this task. By ap...
متن کاملSchur aggregation for linear systems and determinants
We apply our recent preconditioning techniques to the solution of linear systems of equations and computing determinants. We combine these techniques with the Sherman–Morrison–Woodbury formula, its new variations, aggregation, iterative refinement, and advanced algorithms that rapidly compute sums and products either error-free or with the desired high accuracy. Our theoretical and experimental...
متن کاملThe Schur Aggregation for Linear Systems and Determinants
According to our previous theoretical and experimental study, additive preconditioners can be readily computed for ill conditioned matrices, but it is not straightforward how such preconditioners can help us to facilitate the solution of linear systems of equations, computation of determinants, and other fundamental matrix computations. We develop some nontrivial techniques for this task. By ap...
متن کاملTR-2007014: The Schur Aggregation and Extended Iterative Refinement
According to our previous theoretical and experimental study, additive preconditioners can be readily computed for ill conditioned matrices, but application of such preconditioners to facilitating matrix computations, in particular to solving linear systems of equations, is not straightforward. In the present paper we develop some nontrivial techniques for the latter task. By applying the Sherm...
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