Please wait ... |

Link to record
https://umu.diva-portal.org/smash/person.jsf?pid=authority-person:65553 $(function(){PrimeFaces.cw("InputTextarea","widget_formSmash_upper_j_idt142_recordDirectLink",{id:"formSmash:upper:j_idt142:recordDirectLink",widgetVar:"widget_formSmash_upper_j_idt142_recordDirectLink",autoResize:true});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt142_j_idt144",{id:"formSmash:upper:j_idt142:j_idt144",widgetVar:"widget_formSmash_upper_j_idt142_j_idt144",target:"formSmash:upper:j_idt142:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Permanent link

Direct link

Kjelgaard Mikkelsen, Carl Christianorcid.org/0000-0002-9158-1941

Open this publication in new window or tab >>Accurate and efficient constrained molecular dynamics of polymers using Newton's method and special purpose code### López-Villellas, Lorién

### Kjelgaard Mikkelsen, Carl Christian

### Galano-Frutos, Juan José

### Marco-Sola, Santiago

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_0_j_idt208_some",{id:"formSmash:j_idt204:0:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_0_j_idt208_some",multiple:true}); ### Alastruey-Benedé, Jesús

### Ibáñez, Pablo

### Moretó, Miquel

### Sancho, Javier

### García-Risueño, Pablo

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_0_j_idt208_otherAuthors",{id:"formSmash:j_idt204:0:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_0_j_idt208_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt204_0_j_idt208_j_idt222",{id:"formSmash:j_idt204:0:j_idt208:j_idt222",widgetVar:"widget_formSmash_j_idt204_0_j_idt208_j_idt222",onLabel:"Hide others...",offLabel:"Show others..."}); 2023 (English)In: Computer Physics Communications, ISSN 0010-4655, E-ISSN 1879-2944, Vol. 288, article id 108742Article in journal (Refereed) Published
##### Abstract [en]

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

Elsevier, 2023
##### Keywords

molecular dynamics, constraint algorithms, nonlinear equations, newton's method, SHAKE, LINCS
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:umu:diva-208209 (URN)10.1016/j.cpc.2023.108742 (DOI)2-s2.0-85151493578 (Scopus ID)
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_0_j_idt208_j_idt379",{id:"formSmash:j_idt204:0:j_idt208:j_idt379",widgetVar:"widget_formSmash_j_idt204_0_j_idt208_j_idt379",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_0_j_idt208_j_idt385",{id:"formSmash:j_idt204:0:j_idt208:j_idt385",widgetVar:"widget_formSmash_j_idt204_0_j_idt208_j_idt385",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_0_j_idt208_j_idt391",{id:"formSmash:j_idt204:0:j_idt208:j_idt391",widgetVar:"widget_formSmash_j_idt204_0_j_idt208_j_idt391",multiple:true});
#####

##### Funder

Swedish Research CouncileSSENCE - An eScience Collaboration
Available from: 2023-05-11 Created: 2023-05-11 Last updated: 2023-05-11Bibliographically approved

Barcelona Supercomputing Center, Barcelona, Spain.

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

Department of Biochemistry, Molecular and Cellular Biology / Biocomputation and Complex Systems Physics Institute (BIFI), Universidad de Zaragoza, Zaragoza, Spain.

Barcelona Supercomputing Center, Barcelona, Spain; Departament d'Arquitectura de Computadors, Universitat Politècnica de Catalunya (UPC), Barcelona, Spain.

Departamento de Informática e Ingeniería de Sistemas / Aragón Institute for Engineering Research (I3A), Universidad de Zaragoza, Zaragoza, Spain.

Departamento de Informática e Ingeniería de Sistemas / Aragón Institute for Engineering Research (I3A), Universidad de Zaragoza, Zaragoza, Spain.

Barcelona Supercomputing Center, Barcelona, Spain; Departament d'Arquitectura de Computadors, Universitat Politècnica de Catalunya (UPC), Barcelona, Spain.

Department of Biochemistry, Molecular and Cellular Biology / Biocomputation and Complex Systems Physics Institute (BIFI), Universidad de Zaragoza, Zaragoza, Spain.

In molecular dynamics simulations we can often increase the time step by imposing constraints on bond lengths and bond angles. This allows us to extend the length of the time interval and therefore the range of physical phenomena that we can afford to simulate. We examine the existing algorithms and software for solving nonlinear constraint equations in parallel and we explain why it is necessary to advance the state-of-the-art. We present ILVES-PC, a new algorithm for imposing bond constraints on proteins accurately and efficiently. It solves the same system of differential algebraic equations as the celebrated SHAKE algorithm, but ILVES-PC solves the nonlinear constraint equations using Newton’s method rather than the nonlinear Gauss-Seidel method. Moreover, ILVES-PC solves the necessary linear systems using a specialized linear solver that exploits the structure of the protein. ILVES-PC can rapidly solve constraint equations as accurately as the hardware will allow. The run-time of ILVES-PC is proportional to the number of constraints. We have integrated ILVES-PC into GROMACS and simulated proteins of different sizes. Compared with SHAKE, we have achieved speedups of up to 4.9× in single-threaded executions and up to 76× in shared-memory multi-threaded executions. Moreover, ILVES-PC is more accurate than P-LINCS algorithm. Our work is a proof-of-concept of the utility of software designed specifically for the simulation of polymers.

Open this publication in new window or tab >>How accurate does Newton have to be?### Kjelgaard Mikkelsen, Carl Christian

### López-Villellas, Lorién

### García-Risueño, Pablo

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_1_j_idt208_some",{id:"formSmash:j_idt204:1:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_1_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_1_j_idt208_otherAuthors",{id:"formSmash:j_idt204:1:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_1_j_idt208_otherAuthors",multiple:true}); 2023 (English)In: Parallel processing and applied mathematics: 14th International conference, PPAM 2022, Gdansk, Poland, September 11–14, 2022, revised selected papers, part I / [ed] Roman Wyrzykowski; Jack Dongarra; Ewa Deelman; Konrad Karczewski, Switzerland: Springer Nature, 2023, Vol. 1, p. 3-15Chapter in book (Refereed)
##### Abstract [en]

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

Switzerland: Springer Nature, 2023
##### Series

Lecture Notes in Computer Science, ISSN 0302-9743, E-ISSN 1611-3349 ; 13826
##### Keywords

systems of nonlinear equations, quasi-Newton methods, approxomation error, rounding error, convergence, stagnation
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:umu:diva-208210 (URN)10.1007/978-3-031-30442-2_1 (DOI)2-s2.0-85161395821 (Scopus ID)978-3-031-30441-5 (ISBN)978-3-031-30442-2 (ISBN)
##### Conference

PPAM 2022
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_1_j_idt208_j_idt379",{id:"formSmash:j_idt204:1:j_idt208:j_idt379",widgetVar:"widget_formSmash_j_idt204_1_j_idt208_j_idt379",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_1_j_idt208_j_idt385",{id:"formSmash:j_idt204:1:j_idt208:j_idt385",widgetVar:"widget_formSmash_j_idt204_1_j_idt208_j_idt385",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_1_j_idt208_j_idt391",{id:"formSmash:j_idt204:1:j_idt208:j_idt391",widgetVar:"widget_formSmash_j_idt204_1_j_idt208_j_idt391",multiple:true});
#####

##### Funder

eSSENCE - An eScience Collaboration
Available from: 2023-05-11 Created: 2023-05-11 Last updated: 2023-06-28Bibliographically approved

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

Barcelona Supercomputing Center, Barcelona, Spain.

We analyze the convergence of quasi-Newton methods in exact and finite precision arithmetic. In particular, we derive an upper bound for the stagnation level and we show that any sufficiently exact quasi-Newton method will converge quadratically until stagnation. In the absence of sufficient accuracy, we are likely to retain rapid linear convergence. We confirm our analysis by computing square roots and solving bond constraint equations in the context of molecular dynamics. We briefly discuss implications for parallel solvers.

Open this publication in new window or tab >>Newton's method revisited: how accurate do we have to be?### Kjelgaard Mikkelsen, Carl Christian

### López-Villellas, Lorién

### García-Risueño, Pablo

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_2_j_idt208_some",{id:"formSmash:j_idt204:2:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_2_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_2_j_idt208_otherAuthors",{id:"formSmash:j_idt204:2:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_2_j_idt208_otherAuthors",multiple:true}); 2023 (English)In: Concurrency and Computation, ISSN 1532-0626, E-ISSN 1532-0634Article in journal (Refereed) Epub ahead of print
##### Abstract [en]

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

John Wiley & Sons, 2023
##### Keywords

approximation error, convergence, quasi-Newton methods, rounding error, stagnation, systems of nonlinear equations
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:umu:diva-212265 (URN)10.1002/cpe.7853 (DOI)001020863100001 ()2-s2.0-85164157230 (Scopus ID)
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_2_j_idt208_j_idt379",{id:"formSmash:j_idt204:2:j_idt208:j_idt379",widgetVar:"widget_formSmash_j_idt204_2_j_idt208_j_idt379",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_2_j_idt208_j_idt385",{id:"formSmash:j_idt204:2:j_idt208:j_idt385",widgetVar:"widget_formSmash_j_idt204_2_j_idt208_j_idt385",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_2_j_idt208_j_idt391",{id:"formSmash:j_idt204:2:j_idt208:j_idt391",widgetVar:"widget_formSmash_j_idt204_2_j_idt208_j_idt391",multiple:true});
#####

Available from: 2023-07-20 Created: 2023-07-20 Last updated: 2023-09-05

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

Barcelona Supercomputing Center, Barcelona, Spain.

Independent Scholar, Berlin, Germany.

We analyze the convergence of quasi-Newton methods in exact and finite precision arithmetic using three different techniques. We derive an upper bound for the stagnation level and we show that any sufficiently exact quasi-Newton method will converge quadratically until stagnation. In the absence of sufficient accuracy, we are likely to retain rapid linear convergence. We confirm our analysis by computing square roots and solving bond constraint equations in the context of molecular dynamics. In particular, we apply both a symmetric variant and Forsgren's variant of the simplified Newton method. This work has implications for the implementation of quasi-Newton methods regardless of the scale of the calculation or the machine.

Open this publication in new window or tab >>Task‐based, GPU‐accelerated and robust library for solving dense nonsymmetric eigenvalue problems### Myllykoski, Mirko

### Kjelgaard Mikkelsen, Carl Christian

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_3_j_idt208_some",{id:"formSmash:j_idt204:3:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_3_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_3_j_idt208_otherAuthors",{id:"formSmash:j_idt204:3:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_3_j_idt208_otherAuthors",multiple:true}); 2021 (English)In: Concurrency and Computation, ISSN 1532-0626, E-ISSN 1532-0634, Vol. 33, no 11, article id e5915Article in journal (Refereed) Published
##### Abstract [en]

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

John Wiley & Sons, 2021
##### Keywords

eigenvalue problem, parallel computing, task‐based, numerical library
##### National Category

Computer Sciences Computational Mathematics
##### Research subject

Computer Science
##### Identifiers

urn:nbn:se:umu:diva-173924 (URN)10.1002/cpe.5915 (DOI)000555868500001 ()2-s2.0-85089025359 (Scopus ID)
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_3_j_idt208_j_idt379",{id:"formSmash:j_idt204:3:j_idt208:j_idt379",widgetVar:"widget_formSmash_j_idt204_3_j_idt208_j_idt379",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_3_j_idt208_j_idt385",{id:"formSmash:j_idt204:3:j_idt208:j_idt385",widgetVar:"widget_formSmash_j_idt204_3_j_idt208_j_idt385",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_3_j_idt208_j_idt391",{id:"formSmash:j_idt204:3:j_idt208:j_idt391",widgetVar:"widget_formSmash_j_idt204_3_j_idt208_j_idt391",multiple:true});
#####

##### Projects

NLAFET
Available from: 2020-08-06 Created: 2020-08-06 Last updated: 2021-07-14Bibliographically 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).

In this paper, we present the StarNEig library for solving dense nonsymmetric standard and generalized eigenvalue problems. The library is built on top of the StarPU runtime system and targets both shared and distributed memory machines. Some components of the library have support for GPU acceleration. The library currently applies to real matrices with real and complex eigenvalues and all calculations are done using real arithmetic. Support for complex matrices is planned for a future release. This paper is aimed at potential users of the library. We describe the design choices and capabilities of the library, and contrast them to existing software such as LAPACK and ScaLAPACK. StarNEig implements a ScaLAPACK compatibility layer which should assist new users in the transition to StarNEig. We demonstrate the performance of the library with a sample of computational experiments.

Open this publication in new window or tab >>Introduction to StarNEig: A Task-based Library for Solving Nonsymmetric Eigenvalue Problems### Myllykoski, Mirko

### Kjelgaard Mikkelsen, Carl Christian

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_idt204_4_j_idt208_some",{id:"formSmash:j_idt204:4:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_4_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_4_j_idt208_otherAuthors",{id:"formSmash:j_idt204:4:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_4_j_idt208_otherAuthors",multiple:true}); 2020 (English)In: Parallel Processing and Applied Mathematics: Revised Selected Papers, Part I / [ed] Roman Wyrzykowski and Boleslaw Szymanski, Springer, 2020, p. 70-81Conference paper, Published paper (Refereed)
##### Abstract [en]

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

Springer, 2020
##### Series

Lecture Notes in Computer Science, ISSN 0302-9743, E-ISSN 1611-3349 ; 12043
##### Keywords

Eigenvalue problem, Task-based, Library
##### National Category

Computer Sciences
##### Research subject

Computer Science; Mathematics
##### Identifiers

urn:nbn:se:umu:diva-168419 (URN)10.1007/978-3-030-43229-4_7 (DOI)2-s2.0-85083964403 (Scopus ID)978-3-030-43228-7 (ISBN)978-3-030-43229-4 (ISBN)
##### Conference

13th International Conference on Parallel Computing and Applied Mathematics, PPAM 2019, Bialystok, Poland, September 8-11, 2019
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_4_j_idt208_j_idt379",{id:"formSmash:j_idt204:4:j_idt208:j_idt379",widgetVar:"widget_formSmash_j_idt204_4_j_idt208_j_idt379",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_4_j_idt208_j_idt385",{id:"formSmash:j_idt204:4:j_idt208:j_idt385",widgetVar:"widget_formSmash_j_idt204_4_j_idt208_j_idt385",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_4_j_idt208_j_idt391",{id:"formSmash:j_idt204:4:j_idt208:j_idt391",widgetVar:"widget_formSmash_j_idt204_4_j_idt208_j_idt391",multiple:true});
#####

##### Projects

NLAFET
Available from: 2020-02-25 Created: 2020-02-25 Last updated: 2023-03-23Bibliographically 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).

Abstract. In this paper, we present the StarNEig library for solvingdense nonsymmetric (generalized) eigenvalue problems. The library isbuilt on top of the StarPU runtime system and targets both shared anddistributed memory machines. Some components of the library supportGPUs. The library is currently in an early beta state and only real arith-metic is supported. Support for complex data types is planned for afuture release. This paper is aimed at potential users of the library. Wedescribe the design choices and capabilities of the library, and contrastthem to existing software such as ScaLAPACK. StarNEig implements aScaLAPACK compatibility layer that should make it easy for new usersto transition to StarNEig. We demonstrate the performance of the librarywith a small set of computational experiments.

Open this publication in new window or tab >>Parallel Robust Computation of Generalized Eigenvectors of Matrix Pencils### Kjelgaard Mikkelsen, Carl Christian

### Myllykoski, Mirko

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_5_j_idt208_some",{id:"formSmash:j_idt204:5:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_5_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_5_j_idt208_otherAuthors",{id:"formSmash:j_idt204:5:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_5_j_idt208_otherAuthors",multiple:true}); 2020 (English)In: Parallel Processing and Applied Mathematics: Revised Selected Papers, Part I / [ed] Roman Wyrzykowski, Ewa Deelman, Jack Dongarra, Konrad Karczewski, Springer, 2020, p. 58-69Conference paper, Published paper (Refereed)
##### Abstract [en]

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

Springer, 2020
##### Series

Lecture Notes in Computer Science, ISSN 0302-9743, E-ISSN 1611-3349 ; 12043
##### Keywords

Generalized eigenvectors, overflow protection, task-parallelism
##### National Category

Computer Sciences
##### Research subject

Computer Science; Mathematics
##### Identifiers

urn:nbn:se:umu:diva-168416 (URN)10.1007/978-3-030-43229-4_6 (DOI)2-s2.0-85083956421 (Scopus ID)978-3-030-43228-7 (ISBN)978-3-030-43229-4 (ISBN)
##### Conference

13th International Conference on Parallel Processing and Applied Mathematics, PPAM 2019, Bialystok, Poland, September 8-11, 2019
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_5_j_idt208_j_idt379",{id:"formSmash:j_idt204:5:j_idt208:j_idt379",widgetVar:"widget_formSmash_j_idt204_5_j_idt208_j_idt379",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_5_j_idt208_j_idt385",{id:"formSmash:j_idt204:5:j_idt208:j_idt385",widgetVar:"widget_formSmash_j_idt204_5_j_idt208_j_idt385",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_5_j_idt208_j_idt391",{id:"formSmash:j_idt204:5:j_idt208:j_idt391",widgetVar:"widget_formSmash_j_idt204_5_j_idt208_j_idt391",multiple:true});
#####

##### Projects

NLAFET
Available from: 2020-02-25 Created: 2020-02-25 Last updated: 2023-03-24Bibliographically approved

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

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

In this paper we consider the problem of computing generalized eigenvectors of a matrix pencil in real Schur form. In exact arithmetic, this problem can be solved using substitution. In practice, substitution is vulnerable to floating-point overflow. The robust solvers xtgevc in LAPACK prevent overflow by dynamically scaling the eigenvectors.These subroutines are scalar and sequential codes which compute theeigenvectors one by one. In this paper, we discuss how to derive robust algorithms which are blocked and parallel. The new StarNEig librarycontains a robust task-parallel solver Zazamoukh which runs on top of StarPU. Our numerical experiments show that Zazamoukh achieves a super-linear speedup compared with dtgevc for sufficiently large matrices.

Open this publication in new window or tab >>Robust Parallel Eigenvector Computation for the Non-Symmetric Eigenvalue Problem### Schwarz, Angelika Beatrix

### Kjelgaard Mikkelsen, Carl Christian

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_idt204_6_j_idt208_some",{id:"formSmash:j_idt204:6:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_6_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_6_j_idt208_otherAuthors",{id:"formSmash:j_idt204:6:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_6_j_idt208_otherAuthors",multiple:true}); 2020 (English)Report (Other academic)
##### Abstract [en]

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

Umeå universitet, 2020. p. 25
##### Series

Report / UMINF, ISSN 0348-0542 ; 20.02
##### National Category

Computer Sciences
##### Research subject

Computer Science; Mathematics
##### Identifiers

urn:nbn:se:umu:diva-168433 (URN)
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_6_j_idt208_j_idt379",{id:"formSmash:j_idt204:6:j_idt208:j_idt379",widgetVar:"widget_formSmash_j_idt204_6_j_idt208_j_idt379",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_6_j_idt208_j_idt385",{id:"formSmash:j_idt204:6:j_idt208:j_idt385",widgetVar:"widget_formSmash_j_idt204_6_j_idt208_j_idt385",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_6_j_idt208_j_idt391",{id:"formSmash:j_idt204:6:j_idt208:j_idt391",widgetVar:"widget_formSmash_j_idt204_6_j_idt208_j_idt391",multiple:true});
#####

##### Projects

NLAFET
Available from: 2020-02-25 Created: 2020-02-25 Last updated: 2023-03-07Bibliographically approved

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

A standard approach for computing eigenvectors of a non-symmetric matrix reduced to real Schurform relies on a variant of backward substitution. Backward substitution is prone to overflow. To avoid overflow, the LAPACK eigenvector routine DTREVC3 associates every eigenvector with a scaling factor and dynamically rescales an entire eigenvector during the backward substitution such that overflow cannot occur. When many eigenvectors are computed, DTREVC3 applies backward substitution successively for every eigenvector. This corresponds to level-2 BLAS operations and constitutes a bottleneck. This paper redesigns the backward substitution such that the entire computation is cast as tile operations (level-3 BLAS). By replacing LAPACK’s scaling factor with tile-local scaling factors, our solver decouples the tiles and sustains parallel scalability even when a lot of numerical scaling is necessary.

Open this publication in new window or tab >>Robust parallel eigenvector computation for the non-symmetric eigenvalue problem### Schwarz, Angelika Beatrix

### Kjelgaard Mikkelsen, Carl Christian

### Karlsson, Lars

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_7_j_idt208_some",{id:"formSmash:j_idt204:7:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_7_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_7_j_idt208_otherAuthors",{id:"formSmash:j_idt204:7:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_7_j_idt208_otherAuthors",multiple:true}); 2020 (English)In: Parallel Computing, ISSN 0167-8191, E-ISSN 1872-7336, Vol. 100, article id 102707Article in journal (Refereed) Published
##### Abstract [en]

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

Elsevier, 2020
##### Keywords

Overflow protection, Eigenvectors, Real Schur form, Tiled algorithms
##### National Category

Computer Sciences
##### Research subject

Computer Science
##### Identifiers

urn:nbn:se:umu:diva-177534 (URN)10.1016/j.parco.2020.102707 (DOI)000597159800001 ()2-s2.0-85089018373 (Scopus ID)
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_7_j_idt208_j_idt379",{id:"formSmash:j_idt204:7:j_idt208:j_idt379",widgetVar:"widget_formSmash_j_idt204_7_j_idt208_j_idt379",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_7_j_idt208_j_idt385",{id:"formSmash:j_idt204:7:j_idt208:j_idt385",widgetVar:"widget_formSmash_j_idt204_7_j_idt208_j_idt385",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_7_j_idt208_j_idt391",{id:"formSmash:j_idt204:7:j_idt208:j_idt391",widgetVar:"widget_formSmash_j_idt204_7_j_idt208_j_idt391",multiple:true});
#####

##### Projects

NLAFET
##### 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.

A standard approach for computing eigenvectors of a non-symmetric matrix reduced to real Schur form relies on a variant of backward substitution. Backward substitution is prone to overflow. To avoid overflow, the LAPACK eigenvector routine DTREVC3 associates every eigenvector with a scaling factor and dynamically rescales an entire eigenvector during the backward substitution such that overflow cannot occur. When many eigenvectors are computed, DTREVC3 applies backward substitution successively for every eigenvector. This corresponds to level-2 BLAS operations and constitutes a bottleneck. This paper redesigns the backward substitution such that the entire computation is cast as tile operations (level-3 BLAS). By replacing LAPACK’s scaling factor with tile-local scaling factors, our solver decouples the tiles and sustains parallel scalability even when a lot of numerical scaling is necessary.

Preprint version: http://umu.diva-portal.org/smash/record.jsf?pid=diva2%3A1396196&dswid=-7045

Available from: 2020-12-11 Created: 2020-12-11 Last updated: 2023-03-24Bibliographically approvedOpen this publication in new window or tab >>Robust Task-Parallel Solution of the Triangular Sylvester Equation### Schwarz, Angelika Beatrix

### Kjelgaard Mikkelsen, Carl Christian

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_8_j_idt208_some",{id:"formSmash:j_idt204:8:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_8_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_8_j_idt208_otherAuthors",{id:"formSmash:j_idt204:8:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_8_j_idt208_otherAuthors",multiple:true}); 2020 (English)In: Parallel Processing and Applied Mathematics: 13th International Conference, PPAM 2019, Bialystok, Poland, September 8–11, 2019, Revised Selected Papers, Part I / [ed] Roman Wyrzykowski, Ewa Deelman, Jack Dongarra, Konrad Karczewski, Springer, 2020, p. 82-92Conference paper, Published paper (Refereed)
##### Abstract [en]

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

Springer, 2020
##### Series

Lecture Notes in Computer Science, ISSN 0302-9743 ; 12043
##### Keywords

Overflow protection, Task parallelism, Triangular Sylvester equation, Real Schur form
##### National Category

Computer Sciences
##### Research subject

Computer Science
##### Identifiers

urn:nbn:se:umu:diva-159435 (URN)10.1007/978-3-030-43229-4_8 (DOI)2-s2.0-85084010959 (Scopus ID)978-3-030-43228-7 (ISBN)978-3-030-43229-4 (ISBN)
##### Conference

13th International Conference, PPAM 2019, Bialystok, Poland, September 8–11, 2019
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_8_j_idt208_j_idt379",{id:"formSmash:j_idt204:8:j_idt208:j_idt379",widgetVar:"widget_formSmash_j_idt204_8_j_idt208_j_idt379",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_8_j_idt208_j_idt385",{id:"formSmash:j_idt204:8:j_idt208:j_idt385",widgetVar:"widget_formSmash_j_idt204_8_j_idt208_j_idt385",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_8_j_idt208_j_idt391",{id:"formSmash:j_idt204:8:j_idt208:j_idt391",widgetVar:"widget_formSmash_j_idt204_8_j_idt208_j_idt391",multiple:true});
#####

##### Funder

EU, Horizon 2020, 671633
##### Note

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

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

The Bartels-Stewart algorithm is a standard approach to solving the dense Sylvester equation. It reduces the problem to the solution of the triangular Sylvester equation. The triangular Sylvester equation is solved with a variant of backward substitution. Backward substitution is prone to overflow. Overflow can be avoided by dynamic scaling of the solution matrix. An algorithm which prevents overflow is said to be robust. The standard library LAPACK contains the robust scalar sequential solver dtrsyl. This paper derives a robust, level-3 BLAS-based task-parallel solver. By adding overflow protection, our robust solver closes the gap between problems solvable by LAPACK and problems solvable by existing non-robust task-parallel solvers. We demonstrate that our robust solver achieves a performance similar to non-robust solvers.

Originally included in thesis in manuscript form.

Preprint version: https://arxiv.org/abs/1905.10574

Available from: 2019-05-28 Created: 2019-05-28 Last updated: 2023-03-23Bibliographically approvedOpen this publication in new window or tab >>D2.7 Eigenvalue solvers for nonsymmetric problems### Myllykoski, Mirko

### Kjelgaard Mikkelsen, Carl Christian

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

### 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_idt204_9_j_idt208_some",{id:"formSmash:j_idt204:9:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_9_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_9_j_idt208_otherAuthors",{id:"formSmash:j_idt204:9:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_9_j_idt208_otherAuthors",multiple:true}); 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)
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_9_j_idt208_j_idt379",{id:"formSmash:j_idt204:9:j_idt208:j_idt379",widgetVar:"widget_formSmash_j_idt204_9_j_idt208_j_idt379",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_9_j_idt208_j_idt385",{id:"formSmash:j_idt204:9:j_idt208:j_idt385",widgetVar:"widget_formSmash_j_idt204_9_j_idt208_j_idt385",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_9_j_idt208_j_idt391",{id:"formSmash:j_idt204:9:j_idt208:j_idt391",widgetVar:"widget_formSmash_j_idt204_9_j_idt208_j_idt391",multiple:true});
#####

##### Projects

NLAFET
##### Note

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

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

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