A multiprocessor algorithm for the symmetric tridiagonal eigenvalue problem
SIAM Journal on Scientific and Statistical Computing
Solving the symmetric tridiagonal eigenvalues problem on the hypercube
SIAM Journal on Scientific and Statistical Computing
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
ScaLAPACK user's guide
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
SIAM Journal on Scientific Computing
Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
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)
Scalable parallelization of FLAME code via the workqueuing model
ACM Transactions on Mathematical Software (TOMS)
Algorithm 880: A testing infrastructure for symmetric tridiagonal eigensolvers
ACM Transactions on Mathematical Software (TOMS)
Parallel tiled QR factorization for multicore architectures
Concurrency and Computation: Practice & Experience
Performance and Accuracy of LAPACK's Symmetric Tridiagonal Eigensolvers
SIAM Journal on Scientific Computing
Programming matrix algorithms-by-blocks for thread-level parallelism
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
On parallelizing the MRRR algorithm for data-parallel coprocessors
PPAM'09 Proceedings of the 8th international conference on Parallel processing and applied mathematics: Part I
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The computation of eigenvalues and eigenvectors of symmetric tridiagonal matrices arises frequently in applications; often as one of the steps in the solution of Hermitian and symmetric eigenproblems. While several accurate and efficient methods for the tridiagonal eigenproblem exist, their corresponding implementations usually target uni-processors or large distributed memory systems. Our new eigensolver MR^3-SMP is instead specifically designed for multi-core and many-core general purpose processors, which today have effectively replaced uni-processors. We show that in most cases MR^3-SMP is faster and achieves better speedups than state-of-the-art eigensolvers for uni-processors and distributed-memory systems.