A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
A Divide-and-Conquer Algorithm for the Symmetric TridiagonalEigenproblem
SIAM Journal on Matrix Analysis and Applications
The symmetric eigenvalue problem
The symmetric eigenvalue problem
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Orthogonal Eigenvectors and Relative Gaps
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Scientific Computing
The design and implementation of the MRRR algorithm
ACM Transactions on Mathematical Software (TOMS)
Performance and Accuracy of LAPACK's Symmetric Tridiagonal Eigensolvers
SIAM Journal on Scientific Computing
ACM Transactions on Mathematical Software (TOMS)
High-performance parallel computations using python as high-level language
Euro-Par 2010 Proceedings of the 2010 conference on Parallel processing
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The algorithm of Multiple Relatively Robust Representations (MRRR or MR3) computes k eigenvalues and eigenvectors of a symmetric tridiagonal matrix in O(nk) arithmetic operations. Large problems can be effectively tackled with existing distributed-memory parallel implementations of MRRR; small and medium size problems can instead make use of LAPACK's routine xSTEMR. However, xSTEMR is optimized for single-core CPUs, and does not take advantage of today's multi-core and future many-core architectures. In this paper we discuss some of the issues and trade-offs arising in the design of MR3---SMP, an algorithm for multi-core CPUs and SMP systems. Experiments on application matrices indicate that MR3---SMP is both faster and obtains better speedups than all the tridiagonal eigensolvers included in LAPACK and Intel's Math Kernel Library (MKL).