A Task-Based Algorithm for Reordering the Eigenvalues of a Matrix in Real Schur Form

• Published in: Lecture notes in computer science Vol. 10777; pp. 207 - 216
• Main Author: Myllykoski, Mirko
• Format: Book Chapter Conference Proceeding
• Language: English
• Published: Switzerland Springer International Publishing AG 2018; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Computer Science; datalogi; Eigenvalue reordering problem; Shared memory machines; Task based programming
• ISBN: 9783319780238; 3319780239; 3319780247; 9783319780245
• ISSN: 0302-9743; 1611-3349; 1611-3349
• DOI: 10.1007/978-3-319-78024-5_19

A task-based parallel algorithm for reordering the eigenvalues of a matrix in real Schur form is presented. The algorithm is realized on top of the StarPU runtime system. Only the aspects which are relevant for shared memory machines are discussed here, but the implementation can be configured to run on distributed memory machines as well. Various techniques to reduce the overhead and the core idle time are discussed. Computational experiments indicate that the new algorithm is between 1.5 and 6.6 times faster than a state of the art MPI-based implementation found in ScaLAPACK. With medium to large matrices, strong scaling efficiencies above 60% up to 28 CPU cores are reported. The overhead and the core idle time are shown to be negligible with the exception of the smallest matrices and highest core counts.