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Kågström, Bo
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Publications (10 of 97) Show all publications
Dmytryshyn, A., Johansson, S., Kågström, B. & Van Dooren, P. (2020). Geometry of Matrix Polynomial Spaces. Foundations of Computational Mathematics, 20(3), 423-450
Open this publication in new window or tab >>Geometry of Matrix Polynomial Spaces
2020 (English)In: Foundations of Computational Mathematics, ISSN 1615-3375, E-ISSN 1615-3383, Vol. 20, no 3, p. 423-450Article in journal (Refereed) Published
Abstract [en]

We study how small perturbations of general matrix polynomials may change their elementary divisors and minimal indices by constructing the closure hierarchy (stratification) graphs of matrix polynomials' orbits and bundles. To solve this problem, we construct the stratification graphs for the first companion Fiedler linearization of matrix polynomials. Recall that the first companion Fiedler linearization as well as all the Fiedler linearizations is matrix pencils with particular block structures. Moreover, we show that the stratification graphs do not depend on the choice of Fiedler linearization which means that all the spaces of the matrix polynomial Fiedler linearizations have the same geometry (topology). This geometry coincides with the geometry of the space of matrix polynomials. The novel results are illustrated by examples using the software tool StratiGraph extended with associated new functionality.

Place, publisher, year, edition, pages
Springer, 2020
Keywords
Matrix polynomials, Stratifications, Matrix pencils, Fiedler linearization, Canonical structure information, Orbit, Bundle
National Category
Computational Mathematics Computer and Information Sciences
Identifiers
urn:nbn:se:umu:diva-163512 (URN)10.1007/s10208-019-09423-1 (DOI)000531825900002 ()2-s2.0-85068193369 (Scopus ID)
Funder
eSSENCE - An eScience CollaborationSwedish Research Council, E0485301
Available from: 2019-09-24 Created: 2019-09-24 Last updated: 2020-10-15Bibliographically approved
Myllykoski, M., Kjelgaard Mikkelsen, C. C., Schwarz, A. B. & Kågström, B. (2019). D2.7 Eigenvalue solvers for nonsymmetric problems. NLAFET Consortium; Umeå University
Open this publication in new window or tab >>D2.7 Eigenvalue solvers for nonsymmetric problems
2019 (English)Report (Other academic)
Place, publisher, year, edition, pages
NLAFET Consortium; Umeå University, 2019. p. 29
National Category
Computer Sciences
Research subject
Mathematics; Computer Science
Identifiers
urn:nbn:se:umu:diva-168424 (URN)
Projects
NLAFET
Note

This work is c by the NLAFET Consortium, 2015–2019. Its duplication is allowed only for personal, educational, or research uses.

Available from: 2020-02-25 Created: 2020-02-25 Last updated: 2023-03-07Bibliographically approved
Kågström, B., Myllykoski, M., Karlsson, L., Kjelgaard Mikkelsen, C. C., Cayrols, S., Duff, I., . . . Tissot, O. (2019). D7.8 Release of the NLAFET library. NLAFET Consortium; Umeå University
Open this publication in new window or tab >>D7.8 Release of the NLAFET library
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2019 (English)Report (Other academic)
Place, publisher, year, edition, pages
NLAFET Consortium; Umeå University, 2019. p. 27
National Category
Computer Sciences
Research subject
Mathematics; Computer Science
Identifiers
urn:nbn:se:umu:diva-168426 (URN)
Projects
NLAFET
Note

This work is c by the NLAFET Consortium, 2015–2019. Its duplication is allowed only for personal, educational, or research uses.

Available from: 2020-02-25 Created: 2020-02-25 Last updated: 2020-02-27Bibliographically approved
Eljammaly, M., Karlsson, L. & Kågström, B. (2018). An auto-tuning framework for a NUMA-aware Hessenberg reduction algorithm. In: ICPE '18 Companion of the 2018 ACM/SPEC International Conference on Performance Engineering: . Paper presented at International Conference on Performance Engineering (ICPE 2018), Berlin, Germany, April 9-13, 2018 (pp. 5-8). ACM Digital Library
Open this publication in new window or tab >>An auto-tuning framework for a NUMA-aware Hessenberg reduction algorithm
2018 (English)In: ICPE '18 Companion of the 2018 ACM/SPEC International Conference on Performance Engineering, ACM Digital Library, 2018, , p. 4p. 5-8Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
ACM Digital Library, 2018. p. 4
Keywords
Auto-tuning, Tuning framework, Binning, Search space decomposition, Multistage search, Hessenberg reduction, NUMA-aware
National Category
Computer Sciences
Identifiers
urn:nbn:se:umu:diva-154392 (URN)10.1145/3185768.3186304 (DOI)000744421000002 ()2-s2.0-85052016714 (Scopus ID)978-1-4503-5629-9 (ISBN)
Conference
International Conference on Performance Engineering (ICPE 2018), Berlin, Germany, April 9-13, 2018
Available from: 2018-12-17 Created: 2018-12-17 Last updated: 2023-09-05Bibliographically approved
Myllykoski, M., Karlsson, L., Kågström, B., Eljammaly, M., Pranesh, S. & Zounon, M. (2018). D2.6 Prototype Software for Eigenvalue Problem Solvers. NLAFET Consortium; Umeå University
Open this publication in new window or tab >>D2.6 Prototype Software for Eigenvalue Problem Solvers
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2018 (English)Report (Other academic)
Place, publisher, year, edition, pages
NLAFET Consortium; Umeå University, 2018. p. 32
National Category
Computer Sciences
Research subject
Mathematics; Computer Science
Identifiers
urn:nbn:se:umu:diva-170222 (URN)
Projects
NLAFET
Note

Part of: Public Deliverables: WP2 – Dense Linear Systems and Eigenvalue Problem Solvers

Available from: 2020-04-29 Created: 2020-04-29 Last updated: 2020-05-05Bibliographically approved
Adlerborn, B., Karlsson, L. & Kågström, B. (2018). Distributed one-stage Hessenberg-triangular reduction with wavefront scheduling. SIAM Journal on Scientific Computing, 40(2), C157-C180
Open this publication in new window or tab >>Distributed one-stage Hessenberg-triangular reduction with wavefront scheduling
2018 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 40, no 2, p. C157-C180Article in journal (Refereed) Published
Abstract [en]

A novel parallel formulation of Hessenberg-triangular reduction of a regular matrix pair on distributed memory computers is presented. The formulation is based on a sequential cacheblocked algorithm by K degrees agstrom et al. [BIT, 48 (2008), pp. 563 584]. A static scheduling algorithm is proposed that addresses the problem of underutilized processes caused by two-sided updates of matrix pairs based on sequences of rotations. Experiments using up to 961 processes demonstrate that the new formulation is an improvement of the state of the art and also identify factors that limit its scalability.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 2018
Keywords
generalized eigenvalue problem, Hessenberg-triangular reduction, parallel algorithms, wavefront scheduling
National Category
Computational Mathematics
Identifiers
urn:nbn:se:umu:diva-147843 (URN)10.1137/16M1103890 (DOI)000431100400039 ()2-s2.0-85046786506 (Scopus ID)
Available from: 2018-05-18 Created: 2018-05-18 Last updated: 2023-03-24Bibliographically approved
Eljammaly, M., Karlsson, L. & Kågström, B. (2018). On the Tunability of a New Hessenberg Reduction Algorithm Using Parallel Cache Assignment. In: Wyrzykowski R., Dongarra J., Deelman E., Karczewski K. (Ed.), Parallel Processing and Applied Mathematics. PPAM 2017: Part 1. Paper presented at 12th International Conference on Parallel Processing and Applied Mathematics, PPAM 2017, Lublin, Poland, 10–13 September, 2017 (pp. 579-589). Springer
Open this publication in new window or tab >>On the Tunability of a New Hessenberg Reduction Algorithm Using Parallel Cache Assignment
2018 (English)In: Parallel Processing and Applied Mathematics. PPAM 2017: Part 1 / [ed] Wyrzykowski R., Dongarra J., Deelman E., Karczewski K., Springer, 2018, p. 579-589Conference paper, Published paper (Refereed)
Abstract [en]

The reduction of a general dense square matrix to Hessenberg form is a well known first step in many standard eigenvalue solvers. Although parallel algorithms exist, the Hessenberg reduction is one of the bottlenecks in AED, a main part in state-of-the-art software for the distributed multishift QR algorithm. We propose a new NUMA-aware algorithm that fits the context of the QR algorithm and evaluate the sensitivity of its algorithmic parameters. The proposed algorithm is faster than LAPACK for all problem sizes and faster than ScaLAPACK for the relatively small problem sizes typical for AED.

Place, publisher, year, edition, pages
Springer, 2018
Series
Lecture Notes in Computer Science, ISSN 0302-9743, E-ISSN 1611-3349 ; 10777
Keywords
Hessenberg reduction, Parallel cache assignment, NUMA-aware algorithm, Shared-memory, Tunable parameters, Off-line tuning
National Category
Computer Sciences Computational Mathematics
Identifiers
urn:nbn:se:umu:diva-145342 (URN)10.1007/978-3-319-78024-5_50 (DOI)000458563300050 ()2-s2.0-85044775461 (Scopus ID)978-3-319-78023-8 (ISBN)978-3-319-78024-5 (ISBN)
Conference
12th International Conference on Parallel Processing and Applied Mathematics, PPAM 2017, Lublin, Poland, 10–13 September, 2017
Note

Available from: 2018-02-28 Created: 2018-02-28 Last updated: 2023-03-23Bibliographically approved
Eljammaly, M., Karlsson, L. & Kågström, B. (2017). An auto-tuning framework for a NUMA-aware Hessenberg reduction algorithm. Umeå: Department of computing science, Umeå university
Open this publication in new window or tab >>An auto-tuning framework for a NUMA-aware Hessenberg reduction algorithm
2017 (English)Report (Other academic)
Abstract [en]

The performance of a recently developed Hessenberg reduction algorithm greatly depends on the values chosen for its tunable parameters. The search space is huge combined with other complications makes the problem hard to solve effectively with generic methods and tools. We describe a modular auto-tuning framework in which the underlying optimization algorithm is easy to substitute. The framework exposes sub-problems of standard auto-tuning type for which existing generic methods can be reused. The outputs of concurrently executing sub-tuners are assembled by the framework into a solution to the original problem.

Place, publisher, year, edition, pages
Umeå: Department of computing science, Umeå university, 2017. p. 14
Series
Report / UMINF, ISSN 0348-0542 ; 17.19
Keywords
Auto-tuning, Tuning framework, Binning, Search space decomposition, Multistage search, Hessenberg reduction, NUMA-aware
National Category
Computer Sciences
Identifiers
urn:nbn:se:umu:diva-145297 (URN)
Available from: 2018-02-28 Created: 2018-02-28 Last updated: 2018-06-09Bibliographically approved
Dmytryshyn, A., Johansson, S. & Kågström, B. (2017). Canonical structure transitions of system pencils. SIAM Journal on Matrix Analysis and Applications, 38(4), 1249-1267
Open this publication in new window or tab >>Canonical structure transitions of system pencils
2017 (English)In: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, E-ISSN 1095-7162, Vol. 38, no 4, p. 1249-1267Article in journal (Refereed) Published
Abstract [en]

We investigate the changes of the canonical structure information under small perturbations for a system pencil associated with a (generalized) linear time-invariant state-space system. The equivalence class of the pencil is taken with respect to feedback-injection equivalence transformations. The results allow us to track possible changes of important linear system characteristics under small perturbations.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 2017
National Category
Mathematics Computer and Information Sciences
Research subject
business data processing
Identifiers
urn:nbn:se:umu:diva-139924 (URN)10.1137/16M1097857 (DOI)000418665600009 ()2-s2.0-85022337450 (Scopus ID)
Funder
Swedish Research Council, E0485301Swedish Research Council, eSSENCE
Available from: 2017-09-26 Created: 2017-09-26 Last updated: 2023-03-24Bibliographically approved
Kjelgaard Mikkelsen, C. C., Myllykoski, M., Adlerborn, B., Karlsson, L. & Kågström, B. (2017). D2.5 Eigenvalue problem solvers. NLAFET
Open this publication in new window or tab >>D2.5 Eigenvalue problem solvers
Show others...
2017 (English)Report (Other academic)
Place, publisher, year, edition, pages
NLAFET, 2017. p. 28
National Category
Computer Sciences
Research subject
Mathematics; Computer Science
Identifiers
urn:nbn:se:umu:diva-168432 (URN)
Projects
NLAFET
Available from: 2020-02-25 Created: 2020-02-25 Last updated: 2021-12-21Bibliographically approved
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