Computing accurate eigensystems of scaled diagonally dominant matrices
SIAM Journal on Numerical Analysis
A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
Accurate singular values of bidiagonal matrices
SIAM Journal on Scientific and Statistical Computing
A Divide-and-Conquer Algorithm for the Symmetric TridiagonalEigenproblem
SIAM Journal on Matrix Analysis and Applications
Applied numerical linear algebra
Applied numerical linear algebra
Using PLAPACK: parallel linear algebra package
Using PLAPACK: parallel linear algebra package
Computing an Eigenvector with Inverse Iteration
SIAM Review
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.)
For tridiagonals T replace T with LDLt
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Numerical computing with IEEE floating point arithmetic
Numerical computing with IEEE floating point arithmetic
MPI: The Complete Reference
Numerical Linear Algebra for High Performance Computers
Numerical Linear Algebra for High Performance Computers
An updated set of basic linear algebra subprograms (BLAS)
ACM Transactions on Mathematical Software (TOMS)
Faster Numerical Algorithms Via Exception Handling
IEEE Transactions on Computers
LAPACK Working Note 94: A User''s Guide to the BLACS v1.0
LAPACK Working Note 94: A User''s Guide to the BLACS v1.0
A Proposal for a Set of Parallel Basic Linear Algebra Subprograms
A Proposal for a Set of Parallel Basic Linear Algebra Subprograms
LAPACK Working Note 37: Two Dimensional Basic Linear Algebra Communication Subprograms
LAPACK Working Note 37: Two Dimensional Basic Linear Algebra Communication Subprograms
Orthogonal Eigenvectors and Relative Gaps
SIAM Journal on Matrix Analysis and Applications
A Bidiagonal Matrix Determines Its Hyperbolic SVD to Varied Relative Accuracy
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Scientific Computing
Glued Matrices and the MRRR Algorithm
SIAM Journal on Scientific Computing
Algorithm 880: A testing infrastructure for symmetric tridiagonal eigensolvers
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Reduction to condensed forms for symmetric eigenvalue problems on multi-core architectures
PPAM'09 Proceedings of the 8th international conference on Parallel processing and applied mathematics: Part I
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
MR3-SMP: A symmetric tridiagonal eigensolver for multi-core architectures
Parallel Computing
The algorithm of multiple relatively robust representations for multi-core processors
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume Part I
Computing eigenvectors of block tridiagonal matrices based on twisted block factorizations
Journal of Computational and Applied Mathematics
Divide and Conquer on Hybrid GPU-Accelerated Multicore Systems
SIAM Journal on Scientific Computing
Detecting Localization in an Invariant Subspace
SIAM Journal on Scientific Computing
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In the 1990's, Dhillon and Parlett devised the algorithm of multiple relatively robust representations (MRRR) for computing numerically orthogonal eigenvectors of a symmetric tridiagonal matrix T with O(n2) cost. While previous publications related to MRRR focused on theoretical aspects of the algorithm, a documentation of software issues has been missing. In this article, we discuss the design and implementation of the new MRRR version STEGR that will be included in the next LAPACK release. By giving an algorithmic description of MRRR and identifying governing parameters, we hope to make STEGR more easily accessible and suitable for future performance tuning. Furthermore, this should help users understand design choices and tradeoffs when using the code.