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An Extended Set of Fortran Basic Linear Algebra Subprograms
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1986
"... This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrixvector operations which should provide for efficient and portable implementations of algorithms for high performance computers. ..."
Abstract

Cited by 447 (69 self)
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This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrixvector operations which should provide for efficient and portable implementations of algorithms for high performance computers.
A Parallel Implementation of the Nonsymmetric QR Algorithm for Distributed Memory Architectures
 SIAM J. SCI. COMPUT
, 2002
"... One approach to solving the nonsymmetric eigenvalue problem in parallel is to parallelize the QR algorithm. Not long ago, this was widely considered to be a hopeless task. Recent efforts have led to significant advances, although the methods proposed up to now have suffered from scalability problems ..."
Abstract

Cited by 36 (3 self)
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One approach to solving the nonsymmetric eigenvalue problem in parallel is to parallelize the QR algorithm. Not long ago, this was widely considered to be a hopeless task. Recent efforts have led to significant advances, although the methods proposed up to now have suffered from scalability problems. This paper discusses an approach to parallelizingthe QR algorithm that greatly improves scalability. A theoretical analysis indicates that the algorithm is ultimately not scalable, but the nonscalability does not become evident until the matrix dimension is enormous. Experiments on the Intel Paragon system, the IBM SP2 supercomputer, the SGI Origin 2000, and the Intel ASCI Option Red supercomputer are reported.
A Distributed Memory Implementation of the Nonsymmetric QR Algorithm
, 1996
"... The QR algorithm is the crux of the serial nonsymmetric eigenvalue problem. Recent efforts to parallelize this algorithm have made significant advances towards solving the parallel nonsymmetric eigenvalue problem. Most methods to date suffer a scalability problem. In this talk we discuss an approach ..."
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The QR algorithm is the crux of the serial nonsymmetric eigenvalue problem. Recent efforts to parallelize this algorithm have made significant advances towards solving the parallel nonsymmetric eigenvalue problem. Most methods to date suffer a scalability problem. In this talk we discuss an approach for parallelizing QR which overcomes many of the disadvantages to date. We also give insights into what is necessary for a parallel algorithm to work using these strategies. Performance of a parallel implementation on the Intel Paragon TM system is reported. Key Words: Parallel computing, eigenvalue, Schur decomposition, QR algorithm AMS (MOS) Subject Classification: 65F15, 15A18 1 Introduction Over the years many methods for solving the parallel unsymmetric eigenvalue problem have been suggested. Most of these methods have serious drawbacks, either in terms of stability, accuracy, scalability, or requiring extra work. This paper describes a version of the QR algorithm [20] that has s...