TR-2008009: Solving Homogeneous Linear Systems with Weakly Randomized Additive Preprocessing
نویسندگان
چکیده
By combining our weakly randomized preconditioning with aggregation and other known and novel techniques, we facilitate the solution of a homogeneous linear system of equations. We demonstrate the power of this approach and show some extensions.
منابع مشابه
Solving Homogeneous Linear Systems with Weakly Randomized Additive Preprocessing
By combining our weakly randomized preconditioning with aggregation and other known and novel techniques, we facilitate the solution of a homogeneous linear system of equations. We demonstrate the power of this approach and show some extensions.
متن کاملTR-2009014: Randomized Preprocessing of Homogeneous Linear Systems
Our randomized preprocessing enables pivoting-free and orthogonalization-free solution of homogeneous linear systems of equations. In the case of Toeplitz inputs, we decrease the solution time from quadratic to nearly linear, and our tests show dramatic decrease of the CPU time as well. We prove numerical stability of our randomized algorithms and extend our approach to solving nonsingular line...
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Our randomized preprocessing enables pivoting-free and orthogonalization-free solution of homogeneous linear systems of equations, which leads to significant acceleration of the known algorithms in the cases of both general and structured input matrices. E.g., in the case of Toeplitz inputs, we decrease the estimated solution time from quadratic to nearly linear, and our tests show dramatic dec...
متن کاملTR-2007009: Computations in the Null Spaces with Additive Preprocessing
We propose and analyze additive preprocessing for computing the vectors in and bases for the null spaces of matrices. Instead of singular linear systems we solve nonsingular ones that preserve the conditioning properties and the structure of the input matrices. For ill conditioned input we can extend our preprocessing further, to decrease the problem size. Our approach is readily extended to th...
متن کاملRandomized Preprocessing of Homogeneous Linear Systems
Our randomized preprocessing enables pivoting-free and orthogonalization-free solution of homogeneous linear systems of equations. In the case of Toeplitz inputs, we decrease the solution time from quadratic to nearly linear, and our tests show dramatic decrease of the CPU time as well. We prove numerical stability of our randomized algorithms and extend our approach to solving nonsingular line...
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تاریخ انتشار 2016