Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

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