# LAPACK Working Note 168: PDSYEVR. ScaLAPACK's Parallel MRRR Algorithm for the Symmetric Eigenvalue

### Dominic Antonelli and Christof Voemel

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/CSD-05-1399

2005

### http://www.eecs.berkeley.edu/Pubs/TechRpts/2005/CSD-05-1399.pdf

In the 90s, Dhillon and Parlett devised a new algorithm (Multiple Relatively Robust Representations, MRRR) for computing numerically orthogonal eigenvectors of a symmetric tridiagonal matrix
*T* with
*O*(
*n*^2) cost. In this paper, we describe the design of PDSYEVR, a ScaLAPACK implementation of the MRRR algorithm to compute the eigenpairs in parallel. It represents a substantial improvement over the symmetric eigensolver PDSYEVX that is currently in ScaLAPACK and is going to be part of the next ScaLAPACK release.

BibTeX citation:

@techreport{Antonelli:CSD-05-1399, Author = {Antonelli, Dominic and Voemel, Christof}, Title = {LAPACK Working Note 168: PDSYEVR. ScaLAPACK's Parallel MRRR Algorithm for the Symmetric Eigenvalue}, Institution = {EECS Department, University of California, Berkeley}, Year = {2005}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2005/5446.html}, Number = {UCB/CSD-05-1399}, Abstract = {In the 90s, Dhillon and Parlett devised a new algorithm (Multiple Relatively Robust Representations, MRRR) for computing numerically orthogonal eigenvectors of a symmetric tridiagonal matrix <i>T</i> with <i>O</i>(<i>n</i>^2) cost. In this paper, we describe the design of PDSYEVR, a ScaLAPACK implementation of the MRRR algorithm to compute the eigenpairs in parallel. It represents a substantial improvement over the symmetric eigensolver PDSYEVX that is currently in ScaLAPACK and is going to be part of the next ScaLAPACK release.} }

EndNote citation:

%0 Report %A Antonelli, Dominic %A Voemel, Christof %T LAPACK Working Note 168: PDSYEVR. ScaLAPACK's Parallel MRRR Algorithm for the Symmetric Eigenvalue %I EECS Department, University of California, Berkeley %D 2005 %@ UCB/CSD-05-1399 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/2005/5446.html %F Antonelli:CSD-05-1399