Matrices with positive definite Hermitian part: inequalities and linear systems
SIAM Journal on Matrix Analysis and Applications
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations
SIAM Journal on Scientific Computing
Low Rank Solution of Lyapunov Equations
SIAM Journal on Matrix Analysis and Applications
Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control)
Cholesky factorization of band matrices using multithreaded BLAS
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Parallel LU factorization of band matrices on SMP systems
HPCC'06 Proceedings of the Second international conference on High Performance Computing and Communications
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In this paper we present two parallel routines for the LU factorization of band matrices arising in model reduction problems that target SMP architectures. The special properties of these problems often allows the elimination of pivoting during the factorization, and results in a higher efficiency of the parallel routines. Also, the routines aggregate operations during the iteration, exposing a coarser-grain parallelism than their LAPACK counterpart. Experimental results on two different parallel platforms show the benefits of the new approach.