Sparse LU factorization of the Cray T3D

1995 ◽  
pp. 690-696 ◽  
Author(s):  
R. Asenjo ◽  
E. L. Zapata
Keyword(s):  
Lu Factorization

scholarly journals Sign determinancy in LU factorization of P-matrices

1995 ◽  
Vol 217 ◽  
pp. 155-166 ◽  
Author(s):  
Charles R. Johnson ◽  
D.Dale Olesky ◽  
P. van den Driessche
Keyword(s):  
Lu Factorization

scholarly journals Level-3 BLAS and LU Factorization on a Matrix Processor

2008 ◽  
Vol 4 (0) ◽  
pp. 151-166 ◽  
Author(s):  
Ahmed S. Zekri ◽  
Stanislav G. Sedukhin
Keyword(s):  
Lu Factorization ◽  
Level 3

scholarly journals Basker: Parallel sparse LU factorization utilizing hierarchical parallelism and data layouts

2017 ◽  
Vol 68 ◽  
pp. 17-31 ◽  
Author(s):  
Joshua D. Booth ◽  
Nathan D. Ellingwood ◽  
Heidi K. Thornquist ◽  
Sivasankaran Rajamanickam
Keyword(s):  
Lu Factorization ◽  
Data Layouts

scholarly journals Gaussian Elimination versus Greedy Methods for the Synthesis of Linear Reversible Circuits

2021 ◽  
Vol 2 (3) ◽  
pp. 1-26
Author(s):  
Timothée Goubault De Brugière ◽  
Marc Baboulin ◽  
Benoît Valiron ◽  
Simon Martiel ◽  
Cyril Allouche
Keyword(s):  
Quantum Computing ◽  
State Of The Art ◽  
Gaussian Elimination ◽  
Random Operators ◽  
Lu Factorization ◽  
Large Problem ◽  
Computational Costs ◽  
Elimination Algorithm ◽  
Reversible Circuits ◽  
Greedy Methods

Linear reversible circuits represent a subclass of reversible circuits with many applications in quantum computing. These circuits can be efficiently simulated by classical computers and their size is polynomially bounded by the number of qubits, making them a good candidate to deploy efficient methods to reduce computational costs. We propose a new algorithm for synthesizing any linear reversible operator by using an optimized version of the Gaussian elimination algorithm coupled with a tuned LU factorization. We also improve the scalability of purely greedy methods. Overall, on random operators, our algorithms improve the state-of-the-art methods for specific ranges of problem sizes: The custom Gaussian elimination algorithm provides the best results for large problem sizes (n > 150), while the purely greedy methods provide quasi optimal results when n < 30. On a benchmark of reversible functions, we manage to significantly reduce the CNOT count and the depth of the circuit while keeping other metrics of importance (T-count, T-depth) as low as possible.

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