Smale's problems (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Smale's problems" in English language version.

refsWebsite

Global rank English rank

18doi.org

2^nd place

8semanticscholar.org

11^th place

8^th place

8arxiv.org

69^th place

59^th place

4psu.edu

207^th place

136^th place

3harvard.edu

18^th place

17^th place

3nih.gov

4^th place

2zbmath.org

1,923^rd place

1,068^th place

2jstor.org

26^th place

20^th place

2unican.es

low place

1cornell.edu

332^nd place

246^th place

1springer.com

274^th place

309^th place

1recursed.blogspot.com

low place

1cityu.edu.hk

low place

arxiv.org

Perelman, Grigori (2002). "The entropy formula for the Ricci flow and its geometric applications". arXiv:math.DG/0211159.
Perelman, Grigori (2003). "Ricci flow with surgery on three-manifolds". arXiv:math.DG/0303109.
Perelman, Grigori (2003). "Finite extinction time for the solutions to the Ricci flow on certain three-manifolds". arXiv:math.DG/0307245.
Bonatti, C.; Crovisier, S.; Wilkinson, A. (2009). "The C¹-generic diffeomorphism has trivial centralizer". Publications Mathématiques de l'IHÉS. 109: 185–244. arXiv:0804.1416. doi:10.1007/s10240-009-0021-z. S2CID 16212782.
Cucker, Felipe; Bürgisser, Peter (2011). "On a problem posed by Steve Smale". Annals of Mathematics. 174 (3): 1785–1836. arXiv:0909.2114. doi:10.4007/annals.2011.174.3.8. S2CID 706015.
Lairez, Pierre (2016). "A deterministic algorithm to compute approximate roots of polynomial systems in polynomial average time". Foundations of Computational Mathematics. to appear (5): 1265–1292. arXiv:1507.05485. doi:10.1007/s10208-016-9319-7. S2CID 8333924.
Acharjee, S.; Gogoi, U. (2024). "The limit of human intelligence". Heliyon. 10 (12): e32465. arXiv:2310.10792. Bibcode:2024Heliy..1032465A. doi:10.1016/j.heliyon.2024.e32465. PMC 11226777. PMID 38975068.
Colbroke, M. J.; Vegard, A.; Hansen, A. C. (2022). "The difficulty of computing stable and accurate neural networks: On the barriers of deep learning and Smale's 18th problem". Proceedings of the National Academy of Sciences. 119 (12): e2107151119. arXiv:2101.08286. Bibcode:2022PNAS..11907151C. doi:10.1073/pnas.2107151119. PMID 35294283.

cityu.edu.hk

www6.cityu.edu.hk

Smale, Steve. "Mathematical Problems for the Next Century" (PDF).

cornell.edu

math.cornell.edu

Tucker, Warwick (2002). "A Rigorous ODE Solver and Smale's 14th Problem" (PDF). Foundations of Computational Mathematics. 2 (1): 53–117. CiteSeerX 10.1.1.545.3996. doi:10.1007/s002080010018. S2CID 353254.

doi.org

Smale, Steve (1998). "Mathematical Problems for the Next Century". Mathematical Intelligencer. 20 (2): 7–15. CiteSeerX 10.1.1.35.4101. doi:10.1007/bf03025291. S2CID 1331144.
Shub, Michael; Smale, Steve (1995). "On the intractability of Hilbert's Nullstellensatz and an algebraic version of "NP≠P?"". Duke Math. J. 81: 47–54. doi:10.1215/S0012-7094-95-08105-8. Zbl 0882.03040.
Albouy, A.; Kaloshin, V. (2012). "Finiteness of central configurations of five bodies in the plane". Annals of Mathematics. 176: 535–588. doi:10.4007/annals.2012.176.1.10.
Gjerstad, Steven (2013). "Price Dynamics in an Exchange Economy". Economic Theory. 52 (2): 461–500. CiteSeerX 10.1.1.415.3888. doi:10.1007/s00199-011-0651-5. S2CID 15322190.
Hahn, Frank (1962). "A theorem on non-tatonnement stability". Econometrica. 30 (3): 463–469. doi:10.2307/1909889. JSTOR 1909889.
Lindgren, Jussi (2022). "General Equilibrium with Price Adjustments—A Dynamic Programming Approach". Analytics. 1 (1): 27–34. doi:10.3390/analytics1010003.
Asaoka, M.; Irie, K. (2016). "A $C \infty$ closing lemma for Hamiltonian diffeomorphisms of closed surfaces". Geometric and Functional Analysis. 26 (5): 1245–1254. doi:10.1007/s00039-016-0386-3. S2CID 119732514.
Kozlovski, O.; Shen, W.; van Strien, S. (2007). "Density of hyperbolicity in dimension one". Annals of Mathematics. 166: 145–182. doi:10.4007/annals.2007.166.145.
Bonatti, C.; Crovisier, S.; Wilkinson, A. (2009). "The C¹-generic diffeomorphism has trivial centralizer". Publications Mathématiques de l'IHÉS. 109: 185–244. arXiv:0804.1416. doi:10.1007/s10240-009-0021-z. S2CID 16212782.
Tucker, Warwick (2002). "A Rigorous ODE Solver and Smale's 14th Problem" (PDF). Foundations of Computational Mathematics. 2 (1): 53–117. CiteSeerX 10.1.1.545.3996. doi:10.1007/s002080010018. S2CID 353254.
Beltrán, Carlos; Pardo, Luis Miguel (2008). "On Smale's 17th Problem: A Probabilistic Positive answer" (PDF). Foundations of Computational Mathematics. 8 (1): 1–43. CiteSeerX 10.1.1.211.3321. doi:10.1007/s10208-005-0211-0. S2CID 11528635.
Beltrán, Carlos; Pardo, Luis Miguel (2009). "Smale's 17th Problem: Average Polynomial Time to compute affine and projective solutions" (PDF). Journal of the American Mathematical Society. 22 (2): 363–385. Bibcode:2009JAMS...22..363B. doi:10.1090/s0894-0347-08-00630-9.
Beltrán, Carlos; Pardo, Luis Miguel (2011). "Fast Linear Homotopy to Find Approximate Zeros of Polynomial Systems". Foundations of Computational Mathematics. 11 (1): 95–129. doi:10.1007/s10208-010-9078-9.
Cucker, Felipe; Bürgisser, Peter (2011). "On a problem posed by Steve Smale". Annals of Mathematics. 174 (3): 1785–1836. arXiv:0909.2114. doi:10.4007/annals.2011.174.3.8. S2CID 706015.
Lairez, Pierre (2016). "A deterministic algorithm to compute approximate roots of polynomial systems in polynomial average time". Foundations of Computational Mathematics. to appear (5): 1265–1292. arXiv:1507.05485. doi:10.1007/s10208-016-9319-7. S2CID 8333924.
Shub, Michael; Smale, Stephen (1993). "Complexity of Bézout's theorem. I. Geometric aspects". J. Amer. Math. Soc. 6 (2): 459–501. doi:10.2307/2152805. JSTOR 2152805..
Acharjee, S.; Gogoi, U. (2024). "The limit of human intelligence". Heliyon. 10 (12): e32465. arXiv:2310.10792. Bibcode:2024Heliy..1032465A. doi:10.1016/j.heliyon.2024.e32465. PMC 11226777. PMID 38975068.
Colbroke, M. J.; Vegard, A.; Hansen, A. C. (2022). "The difficulty of computing stable and accurate neural networks: On the barriers of deep learning and Smale's 18th problem". Proceedings of the National Academy of Sciences. 119 (12): e2107151119. arXiv:2101.08286. Bibcode:2022PNAS..11907151C. doi:10.1073/pnas.2107151119. PMID 35294283.

harvard.edu

ui.adsabs.harvard.edu

Beltrán, Carlos; Pardo, Luis Miguel (2009). "Smale's 17th Problem: Average Polynomial Time to compute affine and projective solutions" (PDF). Journal of the American Mathematical Society. 22 (2): 363–385. Bibcode:2009JAMS...22..363B. doi:10.1090/s0894-0347-08-00630-9.
Acharjee, S.; Gogoi, U. (2024). "The limit of human intelligence". Heliyon. 10 (12): e32465. arXiv:2310.10792. Bibcode:2024Heliy..1032465A. doi:10.1016/j.heliyon.2024.e32465. PMC 11226777. PMID 38975068.
Colbroke, M. J.; Vegard, A.; Hansen, A. C. (2022). "The difficulty of computing stable and accurate neural networks: On the barriers of deep learning and Smale's 18th problem". Proceedings of the National Academy of Sciences. 119 (12): e2107151119. arXiv:2101.08286. Bibcode:2022PNAS..11907151C. doi:10.1073/pnas.2107151119. PMID 35294283.

jstor.org

Hahn, Frank (1962). "A theorem on non-tatonnement stability". Econometrica. 30 (3): 463–469. doi:10.2307/1909889. JSTOR 1909889.
Shub, Michael; Smale, Stephen (1993). "Complexity of Bézout's theorem. I. Geometric aspects". J. Amer. Math. Soc. 6 (2): 459–501. doi:10.2307/2152805. JSTOR 2152805..

nih.gov

pubmed.ncbi.nlm.nih.gov

Acharjee, S.; Gogoi, U. (2024). "The limit of human intelligence". Heliyon. 10 (12): e32465. arXiv:2310.10792. Bibcode:2024Heliy..1032465A. doi:10.1016/j.heliyon.2024.e32465. PMC 11226777. PMID 38975068.
Colbroke, M. J.; Vegard, A.; Hansen, A. C. (2022). "The difficulty of computing stable and accurate neural networks: On the barriers of deep learning and Smale's 18th problem". Proceedings of the National Academy of Sciences. 119 (12): e2107151119. arXiv:2101.08286. Bibcode:2022PNAS..11907151C. doi:10.1073/pnas.2107151119. PMID 35294283.

ncbi.nlm.nih.gov

Acharjee, S.; Gogoi, U. (2024). "The limit of human intelligence". Heliyon. 10 (12): e32465. arXiv:2310.10792. Bibcode:2024Heliy..1032465A. doi:10.1016/j.heliyon.2024.e32465. PMC 11226777. PMID 38975068.

psu.edu

citeseerx.ist.psu.edu

Smale, Steve (1998). "Mathematical Problems for the Next Century". Mathematical Intelligencer. 20 (2): 7–15. CiteSeerX 10.1.1.35.4101. doi:10.1007/bf03025291. S2CID 1331144.
Gjerstad, Steven (2013). "Price Dynamics in an Exchange Economy". Economic Theory. 52 (2): 461–500. CiteSeerX 10.1.1.415.3888. doi:10.1007/s00199-011-0651-5. S2CID 15322190.
Tucker, Warwick (2002). "A Rigorous ODE Solver and Smale's 14th Problem" (PDF). Foundations of Computational Mathematics. 2 (1): 53–117. CiteSeerX 10.1.1.545.3996. doi:10.1007/s002080010018. S2CID 353254.
Beltrán, Carlos; Pardo, Luis Miguel (2008). "On Smale's 17th Problem: A Probabilistic Positive answer" (PDF). Foundations of Computational Mathematics. 8 (1): 1–43. CiteSeerX 10.1.1.211.3321. doi:10.1007/s10208-005-0211-0. S2CID 11528635.

recursed.blogspot.com

"Tucson - Day 3 - Interview with Steve Smale". Recursivity. February 3, 2006.

semanticscholar.org

api.semanticscholar.org

Smale, Steve (1998). "Mathematical Problems for the Next Century". Mathematical Intelligencer. 20 (2): 7–15. CiteSeerX 10.1.1.35.4101. doi:10.1007/bf03025291. S2CID 1331144.
Gjerstad, Steven (2013). "Price Dynamics in an Exchange Economy". Economic Theory. 52 (2): 461–500. CiteSeerX 10.1.1.415.3888. doi:10.1007/s00199-011-0651-5. S2CID 15322190.
Asaoka, M.; Irie, K. (2016). "A $C \infty$ closing lemma for Hamiltonian diffeomorphisms of closed surfaces". Geometric and Functional Analysis. 26 (5): 1245–1254. doi:10.1007/s00039-016-0386-3. S2CID 119732514.
Bonatti, C.; Crovisier, S.; Wilkinson, A. (2009). "The C¹-generic diffeomorphism has trivial centralizer". Publications Mathématiques de l'IHÉS. 109: 185–244. arXiv:0804.1416. doi:10.1007/s10240-009-0021-z. S2CID 16212782.
Tucker, Warwick (2002). "A Rigorous ODE Solver and Smale's 14th Problem" (PDF). Foundations of Computational Mathematics. 2 (1): 53–117. CiteSeerX 10.1.1.545.3996. doi:10.1007/s002080010018. S2CID 353254.
Beltrán, Carlos; Pardo, Luis Miguel (2008). "On Smale's 17th Problem: A Probabilistic Positive answer" (PDF). Foundations of Computational Mathematics. 8 (1): 1–43. CiteSeerX 10.1.1.211.3321. doi:10.1007/s10208-005-0211-0. S2CID 11528635.
Cucker, Felipe; Bürgisser, Peter (2011). "On a problem posed by Steve Smale". Annals of Mathematics. 174 (3): 1785–1836. arXiv:0909.2114. doi:10.4007/annals.2011.174.3.8. S2CID 706015.
Lairez, Pierre (2016). "A deterministic algorithm to compute approximate roots of polynomial systems in polynomial average time". Foundations of Computational Mathematics. to appear (5): 1265–1292. arXiv:1507.05485. doi:10.1007/s10208-016-9319-7. S2CID 8333924.

springer.com

link.springer.com

Beltrán, Carlos; Pardo, Luis Miguel (2011). "Fast Linear Homotopy to Find Approximate Zeros of Polynomial Systems". Foundations of Computational Mathematics. 11 (1): 95–129. doi:10.1007/s10208-010-9078-9.

unican.es

personales.unican.es

Beltrán, Carlos; Pardo, Luis Miguel (2008). "On Smale's 17th Problem: A Probabilistic Positive answer" (PDF). Foundations of Computational Mathematics. 8 (1): 1–43. CiteSeerX 10.1.1.211.3321. doi:10.1007/s10208-005-0211-0. S2CID 11528635.
Beltrán, Carlos; Pardo, Luis Miguel (2009). "Smale's 17th Problem: Average Polynomial Time to compute affine and projective solutions" (PDF). Journal of the American Mathematical Society. 22 (2): 363–385. Bibcode:2009JAMS...22..363B. doi:10.1090/s0894-0347-08-00630-9.

zbmath.org

Shub, Michael; Smale, Steve (1995). "On the intractability of Hilbert's Nullstellensatz and an algebraic version of "NP≠P?"". Duke Math. J. 81: 47–54. doi:10.1215/S0012-7094-95-08105-8. Zbl 0882.03040.
Bürgisser, Peter (2000). Completeness and reduction in algebraic complexity theory. Algorithms and Computation in Mathematics. Vol. 7. Berlin: Springer-Verlag. p. 141. ISBN 978-3-540-66752-0. Zbl 0948.68082.