Computational complexity of mathematical operations (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Computational complexity of mathematical operations" in English language version.

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Tao, Terence (2010). "1.11 The AKS primality test". An epsilon of room, II: Pages from year three of a mathematical blog. Graduate Studies in Mathematics. Vol. 117. American Mathematical Society. pp. 82–86. doi:10.1090/gsm/117. ISBN 978-0-8218-5280-4. MR 2780010.
Morain, F. (2007). "Implementing the asymptotically fast version of the elliptic curve primality proving algorithm". Mathematics of Computation. 76 (257): 493–505. arXiv:math/0502097. Bibcode:2007MaCom..76..493M. doi:10.1090/S0025-5718-06-01890-4. MR 2261033. S2CID 133193.
Baillie, Robert; Wagstaff, Jr., Samuel S. (October 1980). "Lucas Pseudoprimes" (PDF). Mathematics of Computation. 35 (152): 1391–1417. doi:10.1090/S0025-5718-1980-0583518-6. JSTOR 2006406. MR 0583518.
Monier, Louis (1980). "Evaluation and comparison of two efficient probabilistic primality testing algorithms". Theoretical Computer Science. 12 (1): 97–108. doi:10.1016/0304-3975(80)90007-9. MR 0582244.

archives-ouvertes.fr

hal.archives-ouvertes.fr

Harvey, D.; Van Der Hoeven, J. (2021). "Integer multiplication in time O (n log n)" (PDF). Annals of Mathematics. 193 (2): 563–617. doi:10.4007/annals.2021.193.2.4. S2CID 109934776.

arxiv.org

Brent, Richard P. (2014) [1975]. "Multiple-precision zero-finding methods and the complexity of elementary function evaluation". In Traub, J.F. (ed.). Analytic Computational Complexity. Elsevier. pp. 151–176. arXiv:1004.3412. ISBN 978-1-4832-5789-1.
Richard P. Brent (2020), The Borwein Brothers, Pi and the AGM, Springer Proceedings in Mathematics & Statistics, vol. 313, arXiv:1802.07558, doi:10.1007/978-3-030-36568-4, ISBN 978-3-030-36567-7, S2CID 214742997
Brent, Richard P.; Zimmermann, Paul (2010). "An $O(M(n)\log n)$ algorithm for the Jacobi symbol". International Algorithmic Number Theory Symposium. Springer. pp. 83–95. arXiv:1004.2091. doi:10.1007/978-3-642-14518-6_10. ISBN 978-3-642-14518-6. S2CID 7632655.
Morain, F. (2007). "Implementing the asymptotically fast version of the elliptic curve primality proving algorithm". Mathematics of Computation. 76 (257): 493–505. arXiv:math/0502097. Bibcode:2007MaCom..76..493M. doi:10.1090/S0025-5718-06-01890-4. MR 2261033. S2CID 133193.
Alman, Josh; Williams, Virginia Vassilevska (2020), "A Refined Laser Method and Faster Matrix Multiplication", 32nd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2021), pp. 522–539, arXiv:2010.05846, doi:10.1137/1.9781611976465.32, ISBN 978-1-61197-646-5, S2CID 222290442
Le Gall, François (2014), "Powers of tensors and fast matrix multiplication", Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation — ISSAC '14, p. 23, arXiv:1401.7714, Bibcode:2014arXiv1401.7714L, doi:10.1145/2608628.2627493, ISBN 9781450325011, S2CID 353236
Cohn, Henry; Kleinberg, Robert; Szegedy, Balazs; Umans, Chris (2005). "Group-theoretic Algorithms for Matrix Multiplication". Proceedings of the 46th Annual Symposium on Foundations of Computer Science. IEEE. pp. 379–388. arXiv:math.GR/0511460. doi:10.1109/SFCS.2005.39. ISBN 0-7695-2468-0. S2CID 6429088.

books.google.com

Brent, Richard P. (2014) [1975]. "Multiple-precision zero-finding methods and the complexity of elementary function evaluation". In Traub, J.F. (ed.). Analytic Computational Complexity. Elsevier. pp. 151–176. arXiv:1004.3412. ISBN 978-1-4832-5789-1.
Crandall, R.; Pomerance, C. (2005). "Algorithm 9.4.7 (Stehlé-Zimmerman binary-recursive-gcd)". Prime Numbers – A Computational Perspective (2nd ed.). Springer. pp. 471–3. ISBN 978-0-387-28979-3.

dartmouth.edu

math.dartmouth.edu

Lenstra jr., H.W.; Pomerance, Carl (2019). "Primality testing with Gaussian periods" (PDF). Journal of the European Mathematical Society. 21 (4): 1229–69. doi:10.4171/JEMS/861. hdl:21.11116/0000-0005-717D-0.
Pomerance, Carl; Selfridge, John L.; Wagstaff, Jr., Samuel S. (July 1980). "The pseudoprimes to 25·10⁹" (PDF). Mathematics of Computation. 35 (151): 1003–26. doi:10.1090/S0025-5718-1980-0572872-7. JSTOR 2006210.

doi.org

Harvey, D.; Van Der Hoeven, J. (2021). "Integer multiplication in time O (n log n)" (PDF). Annals of Mathematics. 193 (2): 563–617. doi:10.4007/annals.2021.193.2.4. S2CID 109934776.
Klarreich, Erica (December 2019). "Multiplication hits the speed limit". Commun. ACM. 63 (1): 11–13. doi:10.1145/3371387. S2CID 209450552.
Schönhage, Arnold (1980). "Storage Modification Machines". SIAM Journal on Computing. 9 (3): 490–508. doi:10.1137/0209036.
Richard P. Brent (2020), The Borwein Brothers, Pi and the AGM, Springer Proceedings in Mathematics & Statistics, vol. 313, arXiv:1802.07558, doi:10.1007/978-3-030-36568-4, ISBN 978-3-030-36567-7, S2CID 214742997
Sorenson, J. (1994). "Two Fast GCD Algorithms". Journal of Algorithms. 16 (1): 110–144. doi:10.1006/jagm.1994.1006.
Möller N (2008). "On Schönhage's algorithm and subquadratic integer gcd computation" (PDF). Mathematics of Computation. 77 (261): 589–607. Bibcode:2008MaCom..77..589M. doi:10.1090/S0025-5718-07-02017-0.
Brent, Richard P.; Zimmermann, Paul (2010). "An $O(M(n)\log n)$ algorithm for the Jacobi symbol". International Algorithmic Number Theory Symposium. Springer. pp. 83–95. arXiv:1004.2091. doi:10.1007/978-3-642-14518-6_10. ISBN 978-3-642-14518-6. S2CID 7632655.
Borwein, P. (1985). "On the complexity of calculating factorials". Journal of Algorithms. 6 (3): 376–380. doi:10.1016/0196-6774(85)90006-9.
Lenstra jr., H.W.; Pomerance, Carl (2019). "Primality testing with Gaussian periods" (PDF). Journal of the European Mathematical Society. 21 (4): 1229–69. doi:10.4171/JEMS/861. hdl:21.11116/0000-0005-717D-0.
Tao, Terence (2010). "1.11 The AKS primality test". An epsilon of room, II: Pages from year three of a mathematical blog. Graduate Studies in Mathematics. Vol. 117. American Mathematical Society. pp. 82–86. doi:10.1090/gsm/117. ISBN 978-0-8218-5280-4. MR 2780010.
Morain, F. (2007). "Implementing the asymptotically fast version of the elliptic curve primality proving algorithm". Mathematics of Computation. 76 (257): 493–505. arXiv:math/0502097. Bibcode:2007MaCom..76..493M. doi:10.1090/S0025-5718-06-01890-4. MR 2261033. S2CID 133193.
Pomerance, Carl; Selfridge, John L.; Wagstaff, Jr., Samuel S. (July 1980). "The pseudoprimes to 25·10⁹" (PDF). Mathematics of Computation. 35 (151): 1003–26. doi:10.1090/S0025-5718-1980-0572872-7. JSTOR 2006210.
Baillie, Robert; Wagstaff, Jr., Samuel S. (October 1980). "Lucas Pseudoprimes" (PDF). Mathematics of Computation. 35 (152): 1391–1417. doi:10.1090/S0025-5718-1980-0583518-6. JSTOR 2006406. MR 0583518.
Monier, Louis (1980). "Evaluation and comparison of two efficient probabilistic primality testing algorithms". Theoretical Computer Science. 12 (1): 97–108. doi:10.1016/0304-3975(80)90007-9. MR 0582244.
Alman, Josh; Williams, Virginia Vassilevska (2020), "A Refined Laser Method and Faster Matrix Multiplication", 32nd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2021), pp. 522–539, arXiv:2010.05846, doi:10.1137/1.9781611976465.32, ISBN 978-1-61197-646-5, S2CID 222290442
Davie, A.M.; Stothers, A.J. (2013), "Improved bound for complexity of matrix multiplication", Proceedings of the Royal Society of Edinburgh, 143A (2): 351–370, doi:10.1017/S0308210511001648, S2CID 113401430
Le Gall, François (2014), "Powers of tensors and fast matrix multiplication", Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation — ISSAC '14, p. 23, arXiv:1401.7714, Bibcode:2014arXiv1401.7714L, doi:10.1145/2608628.2627493, ISBN 9781450325011, S2CID 353236
Le Gall, François; Urrutia, Floren (2018). "Improved Rectangular Matrix Multiplication using Powers of the Coppersmith-Winograd Tensor". In Czumaj, Artur (ed.). Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics. doi:10.1137/1.9781611975031.67. ISBN 978-1-61197-503-1. S2CID 33396059.
Knight, Philip A. (May 1995). "Fast rectangular matrix multiplication and QR decomposition". Linear Algebra and Its Applications. 221: 69–81. doi:10.1016/0024-3795(93)00230-w. ISSN 0024-3795.
Preparata, F.P.; Sarwate, D.V. (April 1978). "An improved parallel processor bound in fast matrix inversion". Information Processing Letters. 7 (3): 148–150. doi:10.1016/0020-0190(78)90079-0.
Galil, Zvi; Pan, Victor (January 16, 1989). "Parallel evaluation of the determinant and of the inverse of a matrix". Information Processing Letters. 30 (1): 148–150. doi:10.1016/0020-0190(89)90173-7., in which the $O(n^{3})$ term is reduced
Cohn, Henry; Kleinberg, Robert; Szegedy, Balazs; Umans, Chris (2005). "Group-theoretic Algorithms for Matrix Multiplication". Proceedings of the 46th Annual Symposium on Foundations of Computer Science. IEEE. pp. 379–388. arXiv:math.GR/0511460. doi:10.1109/SFCS.2005.39. ISBN 0-7695-2468-0. S2CID 6429088.

free.fr

mpqs.free.fr

Baillie, Robert; Wagstaff, Jr., Samuel S. (October 1980). "Lucas Pseudoprimes" (PDF). Mathematics of Computation. 35 (152): 1391–1417. doi:10.1090/S0025-5718-1980-0583518-6. JSTOR 2006406. MR 0583518.

fu-berlin.de

page.mi.fu-berlin.de

Rote, G. (2001). "Division-free algorithms for the determinant and the pfaffian: algebraic and combinatorial approaches" (PDF). Computational discrete mathematics. Springer. pp. 119–135. ISBN 3-540-45506-X.

handle.net

hdl.handle.net

Lenstra jr., H.W.; Pomerance, Carl (2019). "Primality testing with Gaussian periods" (PDF). Journal of the European Mathematical Society. 21 (4): 1229–69. doi:10.4171/JEMS/861. hdl:21.11116/0000-0005-717D-0.

harvard.edu

ui.adsabs.harvard.edu

Möller N (2008). "On Schönhage's algorithm and subquadratic integer gcd computation" (PDF). Mathematics of Computation. 77 (261): 589–607. Bibcode:2008MaCom..77..589M. doi:10.1090/S0025-5718-07-02017-0.
Morain, F. (2007). "Implementing the asymptotically fast version of the elliptic curve primality proving algorithm". Mathematics of Computation. 76 (257): 493–505. arXiv:math/0502097. Bibcode:2007MaCom..76..493M. doi:10.1090/S0025-5718-06-01890-4. MR 2261033. S2CID 133193.
Le Gall, François (2014), "Powers of tensors and fast matrix multiplication", Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation — ISSAC '14, p. 23, arXiv:1401.7714, Bibcode:2014arXiv1401.7714L, doi:10.1145/2608628.2627493, ISBN 9781450325011, S2CID 353236

jstor.org

Pomerance, Carl; Selfridge, John L.; Wagstaff, Jr., Samuel S. (July 1980). "The pseudoprimes to 25·10⁹" (PDF). Mathematics of Computation. 35 (151): 1003–26. doi:10.1090/S0025-5718-1980-0572872-7. JSTOR 2006210.
Baillie, Robert; Wagstaff, Jr., Samuel S. (October 1980). "Lucas Pseudoprimes" (PDF). Mathematics of Computation. 35 (152): 1391–1417. doi:10.1090/S0025-5718-1980-0583518-6. JSTOR 2006406. MR 0583518.

liu.se

lysator.liu.se

Möller N (2008). "On Schönhage's algorithm and subquadratic integer gcd computation" (PDF). Mathematics of Computation. 77 (261): 589–607. Bibcode:2008MaCom..77..589M. doi:10.1090/S0025-5718-07-02017-0.

scribd.com

Vassilevska Williams, Virginia (2014), Breaking the Coppersmith-Winograd barrier: Multiplying matrices in O(n^2.373) time

semanticscholar.org

api.semanticscholar.org

Harvey, D.; Van Der Hoeven, J. (2021). "Integer multiplication in time O (n log n)" (PDF). Annals of Mathematics. 193 (2): 563–617. doi:10.4007/annals.2021.193.2.4. S2CID 109934776.
Klarreich, Erica (December 2019). "Multiplication hits the speed limit". Commun. ACM. 63 (1): 11–13. doi:10.1145/3371387. S2CID 209450552.
Richard P. Brent (2020), The Borwein Brothers, Pi and the AGM, Springer Proceedings in Mathematics & Statistics, vol. 313, arXiv:1802.07558, doi:10.1007/978-3-030-36568-4, ISBN 978-3-030-36567-7, S2CID 214742997
Brent, Richard P.; Zimmermann, Paul (2010). "An $O(M(n)\log n)$ algorithm for the Jacobi symbol". International Algorithmic Number Theory Symposium. Springer. pp. 83–95. arXiv:1004.2091. doi:10.1007/978-3-642-14518-6_10. ISBN 978-3-642-14518-6. S2CID 7632655.
Morain, F. (2007). "Implementing the asymptotically fast version of the elliptic curve primality proving algorithm". Mathematics of Computation. 76 (257): 493–505. arXiv:math/0502097. Bibcode:2007MaCom..76..493M. doi:10.1090/S0025-5718-06-01890-4. MR 2261033. S2CID 133193.
Alman, Josh; Williams, Virginia Vassilevska (2020), "A Refined Laser Method and Faster Matrix Multiplication", 32nd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2021), pp. 522–539, arXiv:2010.05846, doi:10.1137/1.9781611976465.32, ISBN 978-1-61197-646-5, S2CID 222290442
Davie, A.M.; Stothers, A.J. (2013), "Improved bound for complexity of matrix multiplication", Proceedings of the Royal Society of Edinburgh, 143A (2): 351–370, doi:10.1017/S0308210511001648, S2CID 113401430
Le Gall, François (2014), "Powers of tensors and fast matrix multiplication", Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation — ISSAC '14, p. 23, arXiv:1401.7714, Bibcode:2014arXiv1401.7714L, doi:10.1145/2608628.2627493, ISBN 9781450325011, S2CID 353236
Le Gall, François; Urrutia, Floren (2018). "Improved Rectangular Matrix Multiplication using Powers of the Coppersmith-Winograd Tensor". In Czumaj, Artur (ed.). Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics. doi:10.1137/1.9781611975031.67. ISBN 978-1-61197-503-1. S2CID 33396059.
Cohn, Henry; Kleinberg, Robert; Szegedy, Balazs; Umans, Chris (2005). "Group-theoretic Algorithms for Matrix Multiplication". Proceedings of the 46th Annual Symposium on Foundations of Computer Science. IEEE. pp. 379–388. arXiv:math.GR/0511460. doi:10.1109/SFCS.2005.39. ISBN 0-7695-2468-0. S2CID 6429088.

siam.org

Alman, Josh; Williams, Virginia Vassilevska (2020), "A Refined Laser Method and Faster Matrix Multiplication", 32nd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2021), pp. 522–539, arXiv:2010.05846, doi:10.1137/1.9781611976465.32, ISBN 978-1-61197-646-5, S2CID 222290442

springer.com

link.springer.com

Brent, Richard P.; Zimmermann, Paul (2010). "An $O(M(n)\log n)$ algorithm for the Jacobi symbol". International Algorithmic Number Theory Symposium. Springer. pp. 83–95. arXiv:1004.2091. doi:10.1007/978-3-642-14518-6_10. ISBN 978-3-642-14518-6. S2CID 7632655.

terrytao.wordpress.com

Tao, Terence (2010). "1.11 The AKS primality test". An epsilon of room, II: Pages from year three of a mathematical blog. Graduate Studies in Mathematics. Vol. 117. American Mathematical Society. pp. 82–86. doi:10.1090/gsm/117. ISBN 978-0-8218-5280-4. MR 2780010.

worldcat.org

search.worldcat.org

Schönhage, A.; Grotefeld, A.F.W.; Vetter, E. (1994). Fast Algorithms—A Multitape Turing Machine Implementation. BI Wissenschafts-Verlag. ISBN 978-3-411-16891-0. OCLC 897602049.
Burnikel, Christoph; Ziegler, Joachim (1998). Fast Recursive Division. Forschungsberichte des Max-Planck-Instituts für Informatik. Saarbrücken: MPI Informatik Bibliothek & Dokumentation. OCLC 246319574. MPII-98-1-022.
Borwein, J.; Borwein, P. (1987). Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity. Wiley. ISBN 978-0-471-83138-9. OCLC 755165897.
Knight, Philip A. (May 1995). "Fast rectangular matrix multiplication and QR decomposition". Linear Algebra and Its Applications. 221: 69–81. doi:10.1016/0024-3795(93)00230-w. ISSN 0024-3795.

yp.to

cr.yp.to

Bernstein, D.J. "Faster Algorithms to Find Non-squares Modulo Worst-case Integers".