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Kågström, Bo

Open this publication in new window or tab >>Distributed one-stage Hessenberg-triangular reduction with wavefront scheduling### Adlerborn, Björn

### Karlsson, Lars

### Kågström, Bo

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 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]

##### 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 ()
#####

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Available from: 2018-05-18 Created: 2018-05-18 Last updated: 2018-06-09Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).

Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).

Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).

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.

Open this publication in new window or tab >>An auto-tuning framework for a NUMA-aware Hessenberg reduction algorithm### Eljammaly, Mahmoud

### Karlsson, Lars

### Kågström, Bo

Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 2017 (English)Report (Other academic)
##### Abstract [en]

##### 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)
#####

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Available from: 2018-02-28 Created: 2018-02-28 Last updated: 2018-06-09Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Computing Science.

Umeå University, Faculty of Science and Technology, Department of Computing Science.

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.

Open this publication in new window or tab >>Canonical structure transitions of system pencils### Dmytryshyn, Andrii

Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).### Johansson, Stefan

Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).### Kågström, Bo

Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 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]

##### Place, publisher, year, edition, pages

Society for Industrial and Applied Mathematics, 2017
##### National Category

Mathematics Computer and Information Sciences
##### Research subject

Computing Science
##### Identifiers

urn:nbn:se:umu:diva-139924 (URN)10.1137/16M1097857 (DOI)000418665600009 ()
#####

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##### Funder

Swedish Research Council, E0485301Swedish Research Council, eSSENCE
Available from: 2017-09-26 Created: 2017-09-26 Last updated: 2018-06-09Bibliographically approved

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.

Open this publication in new window or tab >>On the Tunability of a New Hessenberg Reduction Algorithm Using Parallel Cache Assignment### Eljammaly, Mahmoud

### Karlsson, Lars

### Kågström, Bo

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 2017 (English)Conference paper, Published paper (Refereed)
##### National Category

Computer Sciences Computational Mathematics
##### Identifiers

urn:nbn:se:umu:diva-145342 (URN)
##### Conference

12th International Conference on Parallel Processing and Applied Mathematics (PPAM 2017)
#####

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##### Note

Umeå University, Faculty of Science and Technology, Department of Computing Science.

Umeå University, Faculty of Science and Technology, Department of Computing Science.

Umeå University, Faculty of Science and Technology, Department of Computing Science.

Accepted for publishing

Available from: 2018-02-28 Created: 2018-02-28 Last updated: 2018-06-09Open this publication in new window or tab >>Distributed one-stage Hessenberg-triangular reduction with wavefront scheduling### Adlerborn, Björn

Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).### Kågström, Bo

Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).### Karlsson, Lars

Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 2016 (English)Report (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Umeå: Department of Computing Science, Umeå University, 2016. p. 26
##### Series

Report / UMINF, ISSN 0348-0542 ; 16.10
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:umu:diva-120002 (URN)
#####

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Available from: 2016-05-04 Created: 2016-05-04 Last updated: 2018-06-07Bibliographically approved

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 cache-blocked algorithm by Kågstrom, Kressner, E.S. Quintana-Ortí, and G. Quintana-Ortí (2008). 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 algorithm is an improvement of the state of the art but also identifies factors that currently limit its scalability.

Open this publication in new window or tab >>Evaluation of the Tunability of a New NUMA-Aware Hessenberg Reduction Algorithm### Eljammaly, Mahmoud

### Karlsson, Lars

Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).### Kågström, Bo

Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 2016 (English)Report (Other academic)
##### Series

Report / UMINF, ISSN 0348-0542 ; 16.21
##### National Category

Computer Sciences
##### Identifiers

urn:nbn:se:umu:diva-152576 (URN)
#####

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Available from: 2018-10-14 Created: 2018-10-14 Last updated: 2018-10-14

Umeå University, Faculty of Science and Technology, Department of Computing Science.

Open this publication in new window or tab >>Algorithm 953: Parallel Library Software for the Multishift QR Algorithm with Aggressive Early Deflation### Granat, Robert

Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).### Kagstrom, Bo

### Kressner, Daniel

### Shao, Meiyue

Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 2015 (English)In: ACM Transactions on Mathematical Software, ISSN 0098-3500, E-ISSN 1557-7295, Vol. 41, no 4, article id 29Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Algorithms, Performance, Multishift QR algorithm, aggressive early deflation, parallel algorithms, stributed memory architectures
##### National Category

Computer Sciences
##### Identifiers

urn:nbn:se:umu:diva-111765 (URN)10.1145/2699471 (DOI)000363733000007 ()2-s2.0-84943313977 (Scopus ID)
#####

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Available from: 2015-11-25 Created: 2015-11-23 Last updated: 2018-06-07Bibliographically approved

Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N). Umeå University, Faculty of Science and Technology, Department of Computing Science.

Library software implementing a parallel small-bulge multishift QR algorithm with Aggressive Early Deflation (AED) targeting distributed memory high-performance computing systems is presented. Starting from recent developments of the parallel multishift QR algorithm [Granat et al., SIAM J. Sci. Comput. 32(4), 2010], we describe a number of algorithmic and implementation improvements. These include communication avoiding algorithms via data redistribution and a refined strategy for balancing between multishift QR sweeps and AED. Guidelines concerning several important tunable algorithmic parameters are provided. As a result of these improvements, a computational bottleneck within AED has been removed in the parallel multishift QR algorithm. A performance model is established to explain the scalability behavior of the new parallel multishift QR algorithm. Numerous computational experiments confirm that our new implementation significantly outperforms previous parallel implementations of the QR algorithm.

Open this publication in new window or tab >>Canonical structure transitions of system pencils### Dmytryshyn, Andrii

### Johansson, Stefan

### Kågström, Bo

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 2015 (English)Report (Other academic)
##### Abstract [en]

##### Publisher

p. 26
##### Series

Report / UMINF, ISSN 0348-0542 ; 15.15
##### Keywords

linear system, descriptor system, state-space system, system pencil, matrix pencil, orbit, bundle, perturbation, versal deformation, stratification
##### National Category

Mathematics Computer and Information Sciences Electrical Engineering, Electronic Engineering, Information Engineering Civil Engineering
##### Identifiers

urn:nbn:se:umu:diva-111632 (URN)
#####

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##### Funder

eSSENCE - An eScience CollaborationSwedish Research Council, E048530
Available from: 2015-11-18 Created: 2015-11-18 Last updated: 2018-06-07Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Computing Science.

Umeå University, Faculty of Science and Technology, Department of Computing Science.

Umeå University, Faculty of Science and Technology, Department of Computing Science.

We investigate the changes under small perturbations of the canonical structure information for a system pencil (A B C D) − s (E 0 0 0), det(E) ≠ 0, associated with a (generalized) linear time-invariant state-space system. The equivalence class of the pencil is taken with respect to feedback-injection equivalence transformation. The results allow to track possible changes under small perturbations of important linear system characteristics.

Open this publication in new window or tab >>Change of the congruence canonical form of 2-by-2 and 3-by-3 matrices under perturbations and bundles of matrices under congruence### Dmytryshyn, Andrii

Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).### Futorny, Vyacheslav

### Kågström, Bo

Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).### Klimenko, Lena

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); ### Sergeichuk, Vladimir

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_8_j_idt188_j_idt202",{id:"formSmash:j_idt184:8:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2015 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 469, p. 305-334Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Bundle, Closure graph, Congruence canonical form, Congruence class, Perturbation
##### National Category

Mathematics
##### Research subject

Mathematics; Computing Science
##### Identifiers

urn:nbn:se:umu:diva-101053 (URN)10.1016/j.laa.2014.11.004 (DOI)000348883600014 ()2-s2.0-84919935890 (Scopus ID)
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##### Funder

eSSENCE - An eScience CollaborationSwedish Research Council, A0581501
Available from: 2015-03-18 Created: 2015-03-18 Last updated: 2018-06-07Bibliographically approved

University of Sao Paulo, Brazil .

Kiev Polytechnic Institute, Ukraine.

Institute of Mathematics, Kiev, Ukraine.

We construct the Hasse diagrams G_{2} and G_{3} for the closure ordering on the sets of congruence classes of 2 × 2 and 3 × 3 complex matrices. In other words, we construct two directed graphs whose vertices are 2 × 2 or, respectively, 3 × 3 canonical matrices under congruence, and there is a directed path from A to B if and only if A can be transformed by an arbitrarily small perturbation to a matrix that is congruent to B. A bundle of matrices under congruence is defined as a set of square matrices A for which the pencils A + λA^{T} belong to the same bundle under strict equivalence. In support of this definition, we show that all matrices in a congruence bundle of 2 × 2 or 3 × 3 matrices have the same properties with respect to perturbations. We construct the Hasse diagrams G_{2} ^{B} and G_{3} ^{B} for the closure ordering on the sets of congruence bundles of 2 × 2 and, respectively, 3 × 3 matrices. We find the isometry groups of 2 × 2 and 3 × 3 congruence canonical matrices.

Open this publication in new window or tab >>Coupled Sylvester-type Matrix Equations and Block Diagonalization### Dmytryshyn, Andrii

### Kågstrom, Bo

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_some",{id:"formSmash:j_idt184:9:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_otherAuthors",{id:"formSmash:j_idt184:9:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_otherAuthors",multiple:true}); 2015 (English)In: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, E-ISSN 1095-7162, Vol. 36, no 2, p. 580-593Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

matrix equation, Sylvester equation, Stein equation, Roth's theorem, nsistency, block diagonalization, MMEL JW, 1987, LINEAR ALGEBRA AND ITS APPLICATIONS, V88-9, P139 anat R., 2007, BIT NUMERICAL MATHEMATICS, V47, P763
##### National Category

Computer Sciences Mathematical Analysis
##### Identifiers

urn:nbn:se:umu:diva-107104 (URN)10.1137/151005907 (DOI)000357407800011 ()
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Available from: 2015-09-23 Created: 2015-08-18 Last updated: 2018-06-07Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå Univ, HPC2N, SE-90187 Umeå, Sweden.

Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå Univ, HPC2N, SE-90187 Umeå, Sweden.

We prove Roth-type theorems for systems of matrix equations including an arbitrary mix of Sylvester and $\star$-Sylvester equations, in which the transpose or conjugate transpose of the unknown matrices also appear. In full generality, we derive consistency conditions by proving that such a system has a solution if and only if the associated set of $2 \times 2$ block matrix representations of the equations are block diagonalizable by (linked) equivalence transformations. Various applications leading to several particular cases have already been investigated in the literature, some recently and some long ago. Solvability of these cases follow immediately from our general consistency theory. We also show how to apply our main result to systems of Stein-type matrix equations.