Matrix computations (3rd ed.)
The symmetric eigenvalue problem
The symmetric eigenvalue problem
A new O (N(2)) algorithm for the symmetric tridiagonal eigenvalue/eigenvector problem
A new O (N(2)) algorithm for the symmetric tridiagonal eigenvalue/eigenvector problem
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
SIAM Journal on Scientific Computing
The design and implementation of the MRRR algorithm
ACM Transactions on Mathematical Software (TOMS)
MR3-SMP: A symmetric tridiagonal eigensolver for multi-core architectures
Parallel Computing
Implementations of main algorithms for generalized eigenproblem on GPU accelerator
ICSI'12 Proceedings of the Third international conference on Advances in Swarm Intelligence - Volume Part II
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The eigenvalues and eigenvectors of a symmetric matrix are of interest in a myriad of applications. One of the fastest and most accurate numerical techniques for the eigendecomposition is the Algorithm of Multiple Relatively Robust Representations (MRRR), the first stable algorithm that computes the eigenvalues and eigenvectors of a tridiagonal symmetric matrix in O(n2) arithmetic operations. In this paper we present a parallelization of the MRRR algorithm for data parallel coprocessors using the CUDA programming environment. The results demonstrate the potential of data-parallel coprocessors for scientific computations: compared to routine sstemr, LAPACK's implementation of MRRR, our parallel algorithm provides 10-fold speedups.