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The PUB-library (Paderborn University BSP library) is used for the implementation of the parallel communication.\r\n          </jats:p>"}],"citation":{"chicago":"Bonorden, Olaf, Joachim von zur Gathen, Jürgen Gerhard, and Olaf Müller. “Factoring a Binary Polynomial of Degree over One Million.” <i>ACM SIGSAM Bulletin</i>, 2001, 16–18. <a href=\"https://doi.org/10.1145/504331.504333\">https://doi.org/10.1145/504331.504333</a>.","short":"O. Bonorden, J. von zur Gathen, J. Gerhard, O. Müller, ACM SIGSAM Bulletin (2001) 16–18.","ieee":"O. Bonorden, J. von zur Gathen, J. Gerhard, and O. Müller, “Factoring a binary polynomial of degree over one million,” <i>ACM SIGSAM Bulletin</i>, pp. 16–18, 2001.","apa":"Bonorden, O., von zur Gathen, J., Gerhard, J., &#38; Müller, O. (2001). Factoring a binary polynomial of degree over one million. <i>ACM SIGSAM Bulletin</i>, 16–18. <a href=\"https://doi.org/10.1145/504331.504333\">https://doi.org/10.1145/504331.504333</a>","bibtex":"@article{Bonorden_von zur Gathen_Gerhard_Müller_2001, title={Factoring a binary polynomial of degree over one million}, DOI={<a href=\"https://doi.org/10.1145/504331.504333\">10.1145/504331.504333</a>}, journal={ACM SIGSAM Bulletin}, author={Bonorden, Olaf and von zur Gathen, Joachim and Gerhard, Jürgen and Müller, Olaf}, year={2001}, pages={16–18} }","ama":"Bonorden O, von zur Gathen J, Gerhard J, Müller O. Factoring a binary polynomial of degree over one million. <i>ACM SIGSAM Bulletin</i>. 2001:16-18. doi:<a href=\"https://doi.org/10.1145/504331.504333\">10.1145/504331.504333</a>","mla":"Bonorden, Olaf, et al. “Factoring a Binary Polynomial of Degree over One Million.” <i>ACM SIGSAM Bulletin</i>, 2001, pp. 16–18, doi:<a href=\"https://doi.org/10.1145/504331.504333\">10.1145/504331.504333</a>."},"publication":"ACM SIGSAM Bulletin","user_id":"15415","doi":"10.1145/504331.504333","_id":"23731","language":[{"iso":"eng"}],"page":"16-18","publication_status":"published","date_updated":"2022-01-06T06:55:58Z","author":[{"full_name":"Bonorden, Olaf","last_name":"Bonorden","first_name":"Olaf"},{"last_name":"von zur Gathen","first_name":"Joachim","full_name":"von zur Gathen, Joachim"},{"full_name":"Gerhard, Jürgen","first_name":"Jürgen","last_name":"Gerhard"},{"first_name":"Olaf","last_name":"Müller","full_name":"Müller, Olaf"}],"publication_identifier":{"issn":["0163-5824"]},"title":"Factoring a binary polynomial of degree over one million","status":"public","year":"2001"},{"status":"public","page":"378-388","_id":"18152","user_id":"15415","volume":2064,"citation":{"mla":"Ziegler, Martin, and Vasco Brattka. “A Computable Spectral Theorem.” <i>Proceedings of the 4th Workshop on Computability and Complexity in Analysis (CCA’2000)</i>, vol. 2064, 2001, pp. 378–88, doi:<a href=\"https://doi.org/10.1007/3-540-45335-0_23\">10.1007/3-540-45335-0_23</a>.","bibtex":"@inproceedings{Ziegler_Brattka_2001, place={Berlin, Heidelberg}, title={A Computable Spectral Theorem}, volume={2064}, DOI={<a href=\"https://doi.org/10.1007/3-540-45335-0_23\">10.1007/3-540-45335-0_23</a>}, booktitle={Proceedings of the 4th Workshop on Computability and Complexity in Analysis (CCA’2000)}, author={Ziegler, Martin and Brattka, Vasco}, year={2001}, pages={378–388} }","ama":"Ziegler M, Brattka V. A Computable Spectral Theorem. In: <i>Proceedings of the 4th Workshop on Computability and Complexity in Analysis (CCA’2000)</i>. Vol 2064. Berlin, Heidelberg; 2001:378-388. doi:<a href=\"https://doi.org/10.1007/3-540-45335-0_23\">10.1007/3-540-45335-0_23</a>","ieee":"M. Ziegler and V. Brattka, “A Computable Spectral Theorem,” in <i>Proceedings of the 4th Workshop on Computability and Complexity in Analysis (CCA’2000)</i>, 2001, vol. 2064, pp. 378–388.","apa":"Ziegler, M., &#38; Brattka, V. (2001). A Computable Spectral Theorem. In <i>Proceedings of the 4th Workshop on Computability and Complexity in Analysis (CCA’2000)</i> (Vol. 2064, pp. 378–388). Berlin, Heidelberg. <a href=\"https://doi.org/10.1007/3-540-45335-0_23\">https://doi.org/10.1007/3-540-45335-0_23</a>","chicago":"Ziegler, Martin, and Vasco Brattka. “A Computable Spectral Theorem.” In <i>Proceedings of the 4th Workshop on Computability and Complexity in Analysis (CCA’2000)</i>, 2064:378–88. Berlin, Heidelberg, 2001. <a href=\"https://doi.org/10.1007/3-540-45335-0_23\">https://doi.org/10.1007/3-540-45335-0_23</a>.","short":"M. Ziegler, V. Brattka, in: Proceedings of the 4th Workshop on Computability and Complexity in Analysis (CCA’2000), Berlin, Heidelberg, 2001, pp. 378–388."},"place":"Berlin, Heidelberg","title":"A Computable Spectral Theorem","year":"2001","publication_identifier":{"isbn":["9783540421979","9783540453352"],"issn":["0302-9743"]},"author":[{"last_name":"Ziegler","first_name":"Martin","full_name":"Ziegler, Martin"},{"last_name":"Brattka","first_name":"Vasco","full_name":"Brattka, Vasco"}],"publication_status":"published","date_updated":"2022-01-06T06:53:26Z","intvolume":"      2064","language":[{"iso":"eng"}],"doi":"10.1007/3-540-45335-0_23","publication":"Proceedings of the 4th Workshop on Computability and Complexity in Analysis (CCA'2000)","abstract":[{"lang":"eng","text":"Computing the spectral decomposition of a normal matrix is among the most frequent tasks to numerical mathematics. A vast range of methods are employed to do so, but all of them suffer from instabilities when applied to degenerate matrices, i.e., those having multiple eigenvalues. We investigate the spectral representation's effectivity properties on the sound formal basis of computable analysis. It turns out that in general the eigenvectors cannot be computed from a given matrix. If however the size of the matrix' spectrum (=number of different eigenvalues) is known in advance, it can be diagonalized effectively. Thus, in principle the spectral decomposition can be computed under remarkably weak non-degeneracy conditions."}],"date_created":"2020-08-24T10:14:06Z","type":"conference","department":[{"_id":"63"}]},{"date_created":"2020-08-24T11:29:08Z","type":"conference","department":[{"_id":"63"}],"publication":"Proceedings of the First International Conference on Discrete Models - Combinatorics, Computation and Geometry (DM-CCG'2001)","citation":{"mla":"Ziegler, Martin, and M. Reza Emamy-Khansari. “New Bounds for Hypercube Slicing Numbers.” <i>Proceedings of the First International Conference on Discrete Models - Combinatorics, Computation and Geometry (DM-CCG’2001)</i>, vol. AA, 2001, pp. 155–64.","ama":"Ziegler M, Emamy-Khansari MR. New Bounds for Hypercube Slicing Numbers. In: <i>Proceedings of the First International Conference on Discrete Models - Combinatorics, Computation and Geometry (DM-CCG’2001)</i>. Vol AA. ; 2001:155-164.","bibtex":"@inproceedings{Ziegler_Emamy-Khansari_2001, title={New Bounds for Hypercube Slicing Numbers}, volume={AA}, booktitle={Proceedings of the First International Conference on Discrete Models - Combinatorics, Computation and Geometry (DM-CCG’2001)}, author={Ziegler, Martin and Emamy-Khansari, M. Reza}, year={2001}, pages={155–164} }","apa":"Ziegler, M., &#38; Emamy-Khansari, M. R. (2001). New Bounds for Hypercube Slicing Numbers. In <i>Proceedings of the First International Conference on Discrete Models - Combinatorics, Computation and Geometry (DM-CCG’2001)</i> (Vol. AA, pp. 155–164).","ieee":"M. Ziegler and M. R. Emamy-Khansari, “New Bounds for Hypercube Slicing Numbers,” in <i>Proceedings of the First International Conference on Discrete Models - Combinatorics, Computation and Geometry (DM-CCG’2001)</i>, 2001, vol. AA, pp. 155–164.","short":"M. Ziegler, M.R. Emamy-Khansari, in: Proceedings of the First International Conference on Discrete Models - Combinatorics, Computation and Geometry (DM-CCG’2001), 2001, pp. 155–164.","chicago":"Ziegler, Martin, and M. Reza Emamy-Khansari. “New Bounds for Hypercube Slicing Numbers.” In <i>Proceedings of the First International Conference on Discrete Models - Combinatorics, Computation and Geometry (DM-CCG’2001)</i>, AA:155–64, 2001."},"abstract":[{"text":"What is the maximum number of edges of the d-dimensional hypercube, denoted by S(d,k), that can be sliced by k many hyperplanes? This question on combinatorial properties of Euclidean geometry arising from linear separability considerations in the theory of Perceptrons has become an issue on its own. We use computational and combinatorial methods to obtain new bounds on S(d,k), s<=8. These strengthen earlier results on hypercube cut numbers.","lang":"eng"}],"page":"155-164","language":[{"iso":"eng"}],"_id":"18166","user_id":"15415","volume":"AA","status":"public","title":"New Bounds for Hypercube Slicing Numbers","year":"2001","author":[{"full_name":"Ziegler, Martin","first_name":"Martin","last_name":"Ziegler"},{"full_name":"Emamy-Khansari, M. Reza","first_name":"M. Reza","last_name":"Emamy-Khansari"}],"date_updated":"2022-01-06T06:53:26Z"},{"user_id":"15415","_id":"18168","language":[{"iso":"eng"}],"page":"181-184","date_updated":"2022-01-06T06:53:26Z","author":[{"full_name":"Brattka, Vasco","last_name":"Brattka","first_name":"Vasco"},{"last_name":"Ziegler","first_name":"Martin","full_name":"Ziegler, Martin"}],"year":"2001","status":"public","title":"Turing Computability of (Non-)Linear Optimization","department":[{"_id":"63"}],"type":"conference","date_created":"2020-08-24T11:33:12Z","abstract":[{"text":"We consider the classical LINEAR OPTIMIZATION Problem, but in the Turing rather than the RealRAM model. Asking for mere computability of a function's maximum over some closed domain, we show that the common presumptions 'full-dimensional' and `bounded' in fact cannot be omitted: The sound framework of Recursive Analysis enables us to rigorously prove this folkloristic observation! On the other hand, convexity of this domain may be weakened to connectedness, and even NON-linear functions turn out to be effectively optimizable.","lang":"eng"}],"citation":{"mla":"Brattka, Vasco, and Martin Ziegler. “Turing Computability of (Non-)Linear Optimization.” <i>Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG’01)</i>, 2001, pp. 181–84.","bibtex":"@inproceedings{Brattka_Ziegler_2001, title={Turing Computability of (Non-)Linear Optimization}, booktitle={Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG’01)}, author={Brattka, Vasco and Ziegler, Martin}, year={2001}, pages={181–184} }","ama":"Brattka V, Ziegler M. Turing Computability of (Non-)Linear Optimization. In: <i>Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG’01)</i>. ; 2001:181-184.","ieee":"V. Brattka and M. Ziegler, “Turing Computability of (Non-)Linear Optimization,” in <i>Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG’01)</i>, 2001, pp. 181–184.","apa":"Brattka, V., &#38; Ziegler, M. (2001). Turing Computability of (Non-)Linear Optimization. In <i>Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG’01)</i> (pp. 181–184).","short":"V. Brattka, M. Ziegler, in: Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG’01), 2001, pp. 181–184.","chicago":"Brattka, Vasco, and Martin Ziegler. “Turing Computability of (Non-)Linear Optimization.” In <i>Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG’01)</i>, 181–84, 2001."},"publication":"Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG'01)"},{"has_accepted_license":"1","status":"public","user_id":"15415","ddc":["000"],"page":"275 - 278","_id":"18370","file_date_updated":"2020-08-26T13:08:08Z","citation":{"apa":"Klein, J., &#38; Fischer, M. (2001). Occlusion Culling for Virtual Environments based on the 3D-Sectorgraph. In <i>Proc. of 3. GI-Informatiktage 2001</i> (pp. 275–278). Bad Schussenried.","ieee":"J. Klein and M. Fischer, “Occlusion Culling for Virtual Environments based on the 3D-Sectorgraph,” in <i>Proc. of 3. GI-Informatiktage 2001</i>, 2001, pp. 275–278.","chicago":"Klein, Jan, and Matthias Fischer. “Occlusion Culling for Virtual Environments Based on the 3D-Sectorgraph.” In <i>Proc. of 3. GI-Informatiktage 2001</i>, 275–78. Bad Schussenried, 2001.","short":"J. Klein, M. Fischer, in: Proc. of 3. GI-Informatiktage 2001, Bad Schussenried, 2001, pp. 275–278.","mla":"Klein, Jan, and Matthias Fischer. “Occlusion Culling for Virtual Environments Based on the 3D-Sectorgraph.” <i>Proc. of 3. GI-Informatiktage 2001</i>, 2001, pp. 275–78.","ama":"Klein J, Fischer M. Occlusion Culling for Virtual Environments based on the 3D-Sectorgraph. In: <i>Proc. of 3. GI-Informatiktage 2001</i>. Bad Schussenried; 2001:275-278.","bibtex":"@inproceedings{Klein_Fischer_2001, place={Bad Schussenried}, title={Occlusion Culling for Virtual Environments based on the 3D-Sectorgraph}, booktitle={Proc. of 3. GI-Informatiktage 2001}, author={Klein, Jan and Fischer, Matthias}, year={2001}, pages={275–278} }"},"place":"Bad Schussenried","date_updated":"2022-01-06T06:53:30Z","title":"Occlusion Culling for Virtual Environments based on the 3D-Sectorgraph","year":"2001","author":[{"first_name":"Jan","last_name":"Klein","full_name":"Klein, Jan"},{"full_name":"Fischer, Matthias","last_name":"Fischer","first_name":"Matthias","id":"146"}],"language":[{"iso":"eng"}],"abstract":[{"text":"We present a new approximate occlusion-culling algorithm that in contrast to other algorithms, manages the objects of the scene in a 3D-sectorgraph. For generating a frame, as far as possible only the visible objects are rendered that can be found quickly by an edge of the graph. The algorithm allows a real-time navigation with over 20 frames per second in complex scenes consisting of over 10 millions of polygons. Moreover, approximation errors are very low.","lang":"eng"}],"publication":"Proc. of 3. 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Erfahrungen, Methoden und Instrumente}, publisher={VDI-Gesellschaft Entwicklung Konstruktion Vertrieb (VDI-EKV)}, author={Zimmer, Detmar}, year={2001}, pages={77–87} }","ama":"Zimmer D. Entwicklung eines Getriebemotoren-Baukastens. In: <i>Variantenvielfalt in Produkten Und Prozessen. Erfahrungen, Methoden Und Instrumente</i>. VDI-Gesellschaft Entwicklung Konstruktion Vertrieb (VDI-EKV); 2001:77-87.","mla":"Zimmer, Detmar. “Entwicklung Eines Getriebemotoren-Baukastens.” <i>Variantenvielfalt in Produkten Und Prozessen. Erfahrungen, Methoden Und Instrumente</i>, VDI-Gesellschaft Entwicklung Konstruktion Vertrieb (VDI-EKV), 2001, pp. 77–87.","chicago":"Zimmer, Detmar. “Entwicklung Eines Getriebemotoren-Baukastens.” In <i>Variantenvielfalt in Produkten Und Prozessen. Erfahrungen, Methoden Und Instrumente</i>, 77–87. VDI-Gesellschaft Entwicklung Konstruktion Vertrieb (VDI-EKV), 2001.","short":"D. Zimmer, in: Variantenvielfalt in Produkten Und Prozessen. Erfahrungen, Methoden Und Instrumente, VDI-Gesellschaft Entwicklung Konstruktion Vertrieb (VDI-EKV), 2001, pp. 77–87.","ieee":"D. Zimmer, “Entwicklung eines Getriebemotoren-Baukastens,” in <i>Variantenvielfalt in Produkten und Prozessen. Erfahrungen, Methoden und Instrumente</i>, 2001, pp. 77–87.","apa":"Zimmer, D. (2001). Entwicklung eines Getriebemotoren-Baukastens. In <i>Variantenvielfalt in Produkten und Prozessen. Erfahrungen, Methoden und Instrumente</i> (pp. 77–87). VDI-Gesellschaft Entwicklung Konstruktion Vertrieb (VDI-EKV)."},"publication":"Variantenvielfalt in Produkten und Prozessen. Erfahrungen, Methoden und Instrumente"},{"_id":"22322","language":[{"iso":"eng"}],"volume":102,"user_id":"38077","author":[{"last_name":"Zimmer","first_name":"Detmar","full_name":"Zimmer, Detmar","id":"604"}],"status":"public","title":"Kraft- oder Formschluss?","year":"2001","intvolume":"       102","date_updated":"2022-01-06T06:55:31Z","date_created":"2021-06-15T11:07:56Z","department":[{"_id":"9"},{"_id":"146"}],"type":"journal_article","citation":{"bibtex":"@article{Zimmer_2001, title={Kraft- oder Formschluss?}, volume={102}, number={17}, journal={SMM - Schweizer Maschinenmarkt }, author={Zimmer, Detmar}, year={2001} }","ama":"Zimmer D. Kraft- oder Formschluss? <i>SMM - Schweizer Maschinenmarkt </i>. 2001;102(17).","mla":"Zimmer, Detmar. “Kraft- Oder Formschluss?” <i>SMM - Schweizer Maschinenmarkt </i>, vol. 102, no. 17, 2001.","chicago":"Zimmer, Detmar. “Kraft- Oder Formschluss?” <i>SMM - Schweizer Maschinenmarkt </i> 102, no. 17 (2001).","short":"D. 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