Advanced search
Publication Cover
Experimental Mathematics Volume 19, 2010 - Issue 2
Submit an article Journal homepage
92
Views
25
CrossRef citations to date
0
Altmetric
Original Article

High-Accuracy Semidefinite Programming Bounds for Kissing Numbers

Hans D. Mittelmann School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287-1804, USA
&
Frank Vallentin Delft Institute of Applied Mathematics, Technical University of Delft, P.O. Box 5031, 2600 GA Delft, The Netherlands
Pages 175-179 | Published online: 30 Jan 2011

Citations (25)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (2)

Fabrício Caluza Machado & Fernando Mário de Oliveira Filho. (2018) Improving the Semidefinite Programming Bound for the Kissing Number by Exploiting Polynomial Symmetry. Experimental Mathematics 27:3, pages 362-369.
Read now
Alexander Barg & Wei-Hsuan Yu. (2013) New Bounds for Spherical Two-Distance Sets. Experimental Mathematics 22:2, pages 187-194.
Read now

Articles from other publishers (23)

Naser Talebizadeh Sardari & Masoud Zargar. (2023) New upper bounds for spherical codes and packings. Mathematische Annalen.
Crossref
Hiroshi Maehara & Horst Martini. (2022) Kissing Numbers for Balls with Varying Radii. Graphs and Combinatorics 38:6.
Crossref
Henry Cohn & Nicholas Triantafillou. (2021) Dual linear programming bounds for sphere packing via modular forms. Mathematics of Computation 91:333, pages 491-508.
Crossref
Maria Dostert & Alexander Kolpakov. (2021) Kissing number in non-Euclidean spaces of constant sectional curvature. Mathematics of Computation 90:331, pages 2507-2525.
Crossref
Maria Dostert & Alexander Kolpakov. 2021. Extended Abstracts EuroComb 2021. Extended Abstracts EuroComb 2021 574 579 .
Alexey Glazyrin. (2020) Contact graphs of ball packings. Journal of Combinatorial Theory, Series B 145, pages 323-340.
Crossref
P. G. Boyvalenkov, P. D. Dragnev, D. P. Hardin, E. B. Saff & M. M. Stoyanova. (2020) Upper bounds for energies of spherical codes of given cardinality and separation. Designs, Codes and Cryptography 88:9, pages 1811-1826.
Crossref
Sihuang Hu & Gabriele Nebe. (2020) Low dimensional strongly perfect lattices IV: The dual strongly perfect lattices of dimension 16. Journal of Number Theory 208, pages 262-294.
Crossref
Jon Lee & Leo Liberti. (2018) On an SDP relaxation for kissing number. Optimization Letters 14:2, pages 417-422.
Crossref
Ramtin Madani, Abdulrahman Kalbat & Javad Lavaei. (2018) A Low-Complexity Parallelizable Numerical Algorithm for Sparse Semidefinite Programming. IEEE Transactions on Control of Network Systems 5:4, pages 1898-1909.
Crossref
Lukas Trombach & Peter Schwerdtfeger. (2018) Gregory-Newton problem for kissing sticky spheres. Physical Review E 98:3.
Crossref
O. R. Musin. (2018) Towards a proof of the 24-cell conjecture. Acta Mathematica Hungarica 155:1, pages 184-199.
Crossref
Hans D. Mittelmann. 2018. Numerical Analysis and Optimization. Numerical Analysis and Optimization 193 208 .
Mioara Joldes, Jean-Michel Muller & Valentina Popescu. (2017) Implementation and Performance Evaluation of an Extended Precision Floating-Point Arithmetic Library for High-Accuracy Semidefinite Programming. Implementation and Performance Evaluation of an Extended Precision Floating-Point Arithmetic Library for High-Accuracy Semidefinite Programming.
Etienne de Klerk & Frank Vallentin. (2016) On the Turing Model Complexity of Interior Point Methods for Semidefinite Programming. SIAM Journal on Optimization 26:3, pages 1944-1961.
Crossref
Mioara Joldes, Jean-Michel Muller, Valentina Popescu & Warwick Tucker. 2016. Mathematical Software – ICMS 2016. Mathematical Software – ICMS 2016 232 240 .
Cristian Dobre & Juan Vera. (2015) Exploiting symmetry in copositive programs via semidefinite hierarchies. Mathematical Programming 151:2, pages 659-680.
Crossref
Rina Okada, Kazuto Fukuchi & Jun Sakuma. 2015. Machine Learning and Knowledge Discovery in Databases. Machine Learning and Knowledge Discovery in Databases 458 473 .
N. A. Kuklin. (2014) Delsarte method in the problem on kissing numbers in high-dimensional spaces. Proceedings of the Steklov Institute of Mathematics 284:S1, pages 108-123.
Crossref
Christine Bachoc, Dion C. Gijswijt, Alexander Schrijver & Frank Vallentin. 2012. Handbook on Semidefinite, Conic and Polynomial Optimization. Handbook on Semidefinite, Conic and Polynomial Optimization 219 269 .
Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Kazuhiro Kobayashi, Kazuhide Nakata & Maho Nakata. 2012. Handbook on Semidefinite, Conic and Polynomial Optimization. Handbook on Semidefinite, Conic and Polynomial Optimization 687 713 .
Hans D. Mittelmann. 2012. Handbook on Semidefinite, Conic and Polynomial Optimization. Handbook on Semidefinite, Conic and Polynomial Optimization 671 686 .
Henry Cohn, Yang Jiao, Abhinav Kumar & Salvatore Torquato. (2011) Rigidity of spherical codes. Geometry & Topology 15:4, pages 2235-2273.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.