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Cucker, Felipe

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Author ID: cucker.felipe Recent zbMATH articles by "Cucker, Felipe"
Published as: Cucker, F.; Cucker, Felipe; Cucker, Filipe
External Links: MGP · Wikidata · ORCID · GND
Documents Indexed: 145 Publications since 1986, including 12 Books
Reviewing Activity: 5 Reviews
all top 5

Serials

16 Journal of Complexity
8 Foundations of Computational Mathematics
4 Theoretical Computer Science
4 SIAM Journal on Optimization
3 Mathematics of Computation
3 IEEE Transactions on Automatic Control
3 SIAM Journal on Computing
3 Mathematical Programming. Series A. Series B
3 Comptes Rendus. Mathématique. Académie des Sciences, Paris
3 London Mathematical Society Lecture Note Series
2 Journal of Symbolic Computation
2 Information and Computation
2 SIAM Journal on Matrix Analysis and Applications
2 Journal of Logic and Computation
2 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
2 Journal de Mathématiques Pures et Appliquées. Neuvième Série
2 Computational Complexity
2 Journal of the ACM
1 American Mathematical Monthly
1 Communications in Algebra
1 IMA Journal of Numerical Analysis
1 Information Processing Letters
1 Rocky Mountain Journal of Mathematics
1 The Annals of Probability
1 Calcolo
1 The Computer Journal. Section A / Section B
1 Journal of Optimization Theory and Applications
1 Journal of Pure and Applied Algebra
1 The Journal of Symbolic Logic
1 Mathematics of Operations Research
1 Mathematical Systems Theory
1 Mathematische Zeitschrift
1 Numerische Mathematik
1 Zeitschrift für Mathematische Logik und Grundlagen der Mathematik
1 Comptes Rendus Mathématiques de l’Académie des Sciences
1 Advances in Applied Mathematics
1 Bollettino della Unione Matemàtica Italiana. Serie VI. D. Algebra e Geometria
1 Chinese Annals of Mathematics. Series B
1 Annals of Pure and Applied Logic
1 Extracta Mathematicae
1 International Journal of Algebra and Computation
1 European Journal of Operational Research
1 SIAM Journal on Applied Mathematics
1 Bulletin of the American Mathematical Society. New Series
1 Comptes Rendus de l’Académie des Sciences. Série I
1 RAIRO. Informatique Théorique et Applications
1 Applicable Algebra in Engineering, Communication and Computing
1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
1 Numerical Linear Algebra with Applications
1 Mathematical Logic Quarterly (MLQ)
1 Discrete and Continuous Dynamical Systems
1 Theory of Computing Systems
1 Publicaciones Matemáticas del Uruguay
1 Annals of Mathematics. Second Series
1 Journal of the European Mathematical Society (JEMS)
1 Acta Numerica
1 Grundlehren der Mathematischen Wissenschaften
1 Cambridge Monographs on Applied and Computational Mathematics
1 Handbook of Numerical Analysis
1 Journal of Fixed Point Theory and Applications
1 Japanese Journal of Mathematics. 3rd Series
1 MathematicS In Action
1 Forum of Mathematics, Sigma

Publications by Year

Citations contained in zbMATH

105 Publications have been cited 2,224 times in 1,400 Documents Cited by Year
Emergent behavior in flocks. Zbl 1366.91116
Cucker, Felipe; Smale, Steve
342
2007
On the mathematical foundations of learning. Zbl 0983.68162
Cucker, Felipe; Smale, Steve
322
2002
Complexity and real computation: A manifesto. Zbl 0872.68036
Blum, Lenore; Cucker, Felipe; Shub, Mike; Smale, Steve
282
1996
Learning theory. An approximation theory viewpoint. Zbl 1274.41001
Cucker, Felipe; Zhou, Ding Xuan
196
2007
On the mathematics of emergence. Zbl 1166.92323
Cucker, Felipe; Smale, Steve
106
2007
Best choices for regularization parameters in learning theory: on the bias-variance problem. Zbl 1057.68085
Cucker, Felipe; Smale, Steve
78
2002
Flocking in noisy environments. Zbl 1273.91404
Cucker, Felipe; Mordecki, Ernesto
70
2008
Avoiding collisions in flocks. Zbl 1368.93370
Cucker, Felipe; Dong, Jiu-Gang
54
2010
Complexity and real computation. Foreword by Richard M. Karp. Zbl 0948.68068
Blum, Leonore; Cucker, Felipe; Shub, Michael; Smale, Steve
53
1997
On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems. Zbl 1115.15004
Cucker, Felipe; Diao, Huaian; Wei, Yimin
39
2007
Condition. The geometry of numerical algorithms. Zbl 1280.65041
Bürgisser, Peter; Cucker, Felipe
37
2013
A general collision-avoiding flocking framework. Zbl 1368.93261
Cucker, Felipe; Dong, Jiu-Gang
28
2011
On the critical exponent for flocks under hierarchical leadership. Zbl 1202.92089
Cucker, Felipe; Dong, Jiu-Gang
27
2009
Flocking with informed agents. Zbl 1163.93306
Cucker, Felipe; Huepe, Cristián
27
2008
On a problem posed by Steve Smale. Zbl 1248.65047
Bürgisser, Peter; Cucker, Felipe
22
2011
A new condition number for linear programming. Zbl 1072.90564
Cheung, Dennis; Cucker, Felipe
21
2001
Complexity estimates depending on condition and round-off error. Zbl 1065.68533
Cucker, Felipe; Smale, Steve
19
1999
Counting complexity classes for numeric computations. II: Algebraic and semialgebraic sets. Zbl 1149.68029
Bürgisser, Peter; Cucker, Felipe
16
2006
A primal-dual algorithm for solving polyhedral conic systems with a finite-precision machine. Zbl 0996.90052
Cucker, Felipe; Peña, Javier
16
2001
Computing over the reals with addition and order: Higher complexity classes. Zbl 0843.68033
Cucker, Felipe; Koiran, Pascal
16
1995
Modeling language evolution. Zbl 1083.68131
Cucker, Felipe; Smale, Steve; Zhou, Ding-Xuan
15
2004
Separation of complexity classes in Koiran’s weak model. Zbl 0819.68053
Cucker, F.; Shub, M.; Smale, S.
15
1994
The probability that a slightly perturbed numerical analysis problem is difficult. Zbl 1195.65018
Bürgisser, Peter; Cucker, Felipe; Lotz, Martin
14
2008
On the power of real Turing machines over binary inputs. Zbl 0874.68110
Cucker, Felipe; Grigoriev, Dima
14
1997
On the complexity of quantifier elimination: The structural approach. Zbl 0788.68058
Cucker, Felipe
13
1993
Smoothed analysis of complex conic condition numbers. Zbl 1113.65044
Bürgisser, Peter; Cucker, Felipe; Lotz, Martin
12
2006
Smoothed analysis of some condition numbers. Zbl 1198.65084
Cucker, F.; Diao, H.; Wei, Y.
12
2006
Unifying condition numbers for linear programming. Zbl 1082.90061
Cheung, Dennis; Cucker, Felipe; Peña, Javier
12
2003
Algebraic settings for the problem ”P\(\neq\)NP?”. Zbl 0856.68068
Blum, Lenore; Cucker, Felipe; Shub, Mike; Smale, Steve
12
1996
An alternate proof of the continuity of the roots of a polynomial. Zbl 0708.30010
Cucker, Felipe; Corbalan, Antonio Gonzalez
12
1989
On flocks influenced by closest neighbors. Zbl 1354.93069
Cucker, Felipe; Dong, Jiu-Gang
11
2016
A numerical algorithm for zero counting. I: Complexity and accuracy. Zbl 1166.65021
Cucker, Felipe; Krick, Teresa; Malajovich, Gregorio; Wschebor, Mario
11
2008
On the expected condition number of linear programming problems. Zbl 1030.65039
Cucker, Felipe; Wschebor, Mario
11
2003
A polynomial time algorithm for diophantine equations in one variable. Zbl 0920.11085
Cucker, Felipe; Koiran, Pascal; Smale, Steve
11
1999
A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysis. Zbl 1215.65218
Cucker, Felipe; Krick, Teresa; Malajovich, Gregorio; Wschebor, Mario
10
2009
Mixed and componentwise condition numbers for rectangular structured matrices. Zbl 1168.15304
Cucker, Felipe; Diao, Huaian
10
2007
On digital nondeterminism. Zbl 0868.68058
Cucker, F.; Matamala, M.
10
1996
On algorithms for real algebraic plane curves. Zbl 0737.14017
Cucker, Felipe; González-Vega, Laureano; Rossello, Francesc
10
1991
A numerical algorithm for zero counting. III: Randomization and condition. Zbl 1245.65189
Cucker, Felipe; Krick, Teresa; Malajovich, Gregorio; Wschebor, Mario
9
2012
Coverage processes on spheres and condition numbers for linear programming. Zbl 1205.60027
Bürgisser, Peter; Cucker, Felipe; Lotz, Martin
9
2010
On real Turing machines that toss coins. Zbl 0938.68648
Cucker, Felipe; Karpinski, Marek; Koiran, Pascal; Lickteig, Thomas; Werther, Kai
9
1995
\(P_ \mathbb{R}{}\neq{}NC_ \mathbb{R}\). Zbl 0753.68044
Cucker, Felipe
9
1992
Solving linear programs with finite precision. II: Algorithms. Zbl 1105.90042
Cheung, Dennis; Cucker, Felipe
8
2006
Variations by complexity theorists on three themes of Euler, Bézout, Betti, and Poincaré. Zbl 1076.68033
Bürgisser, Peter; Cucker, Felipe
8
2004
Computability over an arbitrary structure. Sequential and parallel polynomial time. Zbl 1029.68056
Bournez, Olivier; Cucker, Felipe; de Naurois, Paulin Jacobé; Marion, Jean-Yves
8
2003
On the computation of the local and global analytic branches of a real algebraic curve. Zbl 0697.14002
Cucker, F.; Pardo, L. M.; Raimondo, M.; Recio, T.; Roy, M. F.
8
1989
A conditional, collision-avoiding, model for swarming. Zbl 1273.93087
Cucker, Felipe; Dong, Jiu-Gang
7
2014
Exotic quantifiers, complexity classes, and complete problems. Zbl 1185.68343
Bürgisser, Peter; Cucker, Felipe
7
2009
Solving linear programs with finite precision. I: Condition numbers and random programs. Zbl 1082.90060
Cheung, Dennis; Cucker, Felipe
7
2004
Two \(P\)-complete problems in the theory of the reals. Zbl 0759.68032
Cucker, F.; Torrecillas, A.
7
1992
Nondeterministic \(\omega\)-computations and the analytical hierarchy. Zbl 0661.03030
Castro, J.; Cucker, F.
7
1989
Counting complexity classes for numeric computations. III: Complex projective sets. Zbl 1100.68032
Bürgisser, Peter; Cucker, Felipe; Lotz, Martin
6
2005
A note on level-2 condition numbers. Zbl 1074.15008
Cheung, Dennis; Cucker, Felipe
6
2005
Probabilistic analysis of condition numbers for linear programming. Zbl 1041.90028
Cheung, D.; Cucker, F.
6
2002
Approximate zeros and condition numbers. Zbl 0967.65063
Cucker, Felipe
6
1999
Logics which capture complexity classes over the reals. Zbl 0933.03047
Cucker, Felipe; Meer, Klaus
5
1999
The arithmetical hierarchy over the reals. Zbl 0765.03020
Cucker, Felipe
5
1992
Condition length and complexity for the solution of polynomial systems. Zbl 1358.65031
Armentano, Diego; Beltrán, Carlos; Bürgisser, Peter; Cucker, Felipe; Shub, Michael
4
2016
Fast computation of zeros of polynomial systems with bounded degree under finite-precision. Zbl 1291.65158
Briquel, Irénée; Cucker, Felipe; Peña, Javier; Roshchina, Vera
4
2014
Smoothed analysis of Moore-Penrose inversion. Zbl 1227.65035
Bürgisser, Peter; Cucker, Felipe
4
2010
The complexity of semilinear problems in succinct representation. Zbl 1113.68057
Bürgisser, Peter; Cucker, Felipe; de Naurois, Paulin Jacobé
4
2006
Tail decay and moment estimates of a condition number for random linear conic systems. Zbl 1097.90057
Cheung, Dennis; Cucker, Felipe; Hauser, Raphael
4
2005
Counting complexity classes for numeric computations. I: Semilinear sets. Zbl 1069.68049
Bürgisser, Peter; Cucker, Felipe
4
2003
Complexity and dimension. Zbl 1337.68117
Cucker, Felipe; Koiran, Pascal; Matamala, Martín
4
1997
A stable, polynomial-time algorithm for the eigenpair problem. Zbl 1401.65034
Armentano, Diego; Beltrán, Carlos; Bürgisser, Peter; Cucker, Felipe; Shub, Michael
3
2018
On strata of degenerate polyhedral cones. I: Condition and distance to strata. Zbl 1163.90644
Cheung, Dennis; Cucker, Felipe; Peña, Javier
3
2009
A condition number for multifold conic systems. Zbl 1168.90572
Cheung, Dennis; Cucker, Felipe; Peña, Javier
3
2008
General formulas for the smoothed analysis of condition numbers. Zbl 1121.65041
Bürgisser, Peter; Cucker, Felipe; Lotz, Martin
3
2006
Implicit complexity over an arbitrary structure: sequential and parallel polynomial time. Zbl 1077.03021
Bounez, Olivier; Cucker, Felipe; Jacobé de Naurois, Paulin; Marion, Jean-Yves
3
2005
The work of Steve Smale on the theory of computation: 1990-1999. Zbl 1050.68042
Cucker, Felipe; Blum, Lenore
3
2002
Generalized Knapsack problems and fixed degree separations. Zbl 0900.68212
Cucker, Felipe; Shub, Michael
3
1996
Time bounded computations over the reals. Zbl 0788.68043
Cucker, F.; Montaña, J. L.; Pardo, L. M.
3
1992
Computing the homology of basic semialgebraic sets in weak exponential time. Zbl 1426.14016
Bürgisser, Peter; Cucker, Felipe; Lairez, Pierre
2
2019
On flocks under switching directed interaction topologies. Zbl 1405.93014
Cucker, Felipe; Dong, Jiu-Gang
2
2019
A randomized homotopy for the Hermitian eigenpair problem. Zbl 1317.65096
Armentano, Diego; Cucker, Felipe
2
2015
Solving second-order conic systems with variable precision. Zbl 1309.90076
Cucker, Felipe; Peña, Javier; Roshchina, Vera
2
2015
A theory of complexity, condition, and roundoff. Zbl 1307.68037
Cucker, Felipe
2
2015
Adversarial smoothed analysis. Zbl 1232.65071
Cucker, Felipe; Hauser, Raphael; Lotz, Martin
2
2010
A note on parallel and alternating time. Zbl 1137.65076
Cucker, Felipe; Briquel, Irénée
2
2007
Implicit complexity over an arbitrary structure: Quantifier alternations. Zbl 1093.68041
Bournez, Olivier; Cucker, Felipe; de Naurois, Paulin Jacobé; Marion, Jean-Yves
2
2006
Counting complexity classes for numeric computations. II. Algebraic and semialgebraic sets. Zbl 1192.68289
Bürgisser, Peter; Cucker, Felipe
2
2004
Real computations with fake numbers. Zbl 1004.68069
Cucker, Felipe
2
2002
There are no sparse NP\(_{w}\)-hard sets. Zbl 0992.68061
Cucker, Felipe; Grigoriev, Dima
2
2001
Real computations with fake numbers. Zbl 0944.03030
Cucker, Felipe
2
1999
NC algorithms for real algebraic numbers. Zbl 0786.12007
Cucker, F.; Lanneau, H.; Mishra, B.; Pedersen, P.; Roy, M.-F.
2
1992
Two P-complete problems in the theory of the reals. Zbl 0785.68038
Cucker, F.; Torrecillas, A.
2
1991
A theorem on random polynomials and some consequences in average complexity. Zbl 0725.12007
Cucker, F.; Roy, M.-F.
2
1990
Sur les anneaux de sections globales du faisceau structural sur le spectre réel. (On the rings of global sections of the structural sheaf over the real spectrum). Zbl 0681.14009
Cucker, Felipe
2
1988
Computing the homology of real projective sets. Zbl 07031361
Cucker, Felipe; Krick, Teresa; Shub, Michael
1
2018
On the condition of the zeros of characteristic polynomials. Zbl 1372.65103
Bürgisser, Peter; Cucker, Felipe; Rocha Cardozo, Elisa
1
2017
Smoothed analysis of componentwise condition numbers for sparse matrices. Zbl 1323.65045
Cheung, Dennis; Cucker, Felipe
1
2015
On the average condition of random linear programs. Zbl 1273.90116
Cheung, Dennis; Cucker, Felipe
1
2013
Manifold mirrors. The crossing paths of the arts and mathematics. Zbl 1300.00023
Cucker, Felipe
1
2013
The legacy of Turing in numerical analysis. Zbl 1274.01074
Cucker, Felipe
1
2012
Systems of polynomial equations. Zbl 1361.65031
Cucker, Felipe; Malajovich, Gregorio
1
2011
On strata of degenerate polyhedral cones. II: Relations between condition measures. Zbl 1273.90214
Cheung, Dennis; Cucker, Felipe; Peña, Javier
1
2010
Foundations of computational mathematics, Hong Kong, China, 2008. Selected papers based on the presentations at the international conference of the Society for the Foundations of Computational Mathematics (FoCM), June 16–26, 2008. Zbl 1170.13001
Cucker, Felipe (ed.); Pinkus, Allan (ed.); Todd, Michael J. (ed.)
1
2009
Safe recursion over an arbitrary structure: PAR, PH and DPH. Zbl 1261.68058
Bournez, Olivier; Cucker, Felipe; De Naurois, Paulin Jacobé; Marion, Jean-Yves
1
2003
Linear programming and condition numbers under the real number computation model. Zbl 1070.65548
Cheung, Dennis; Cucker, Filipe; Ye, Yinyu
1
2003
On weak and weighted computations over the real closure of \(\mathbb{Q}\). Zbl 0977.68034
Cucker, Felipe
1
2001
Computing the homology of basic semialgebraic sets in weak exponential time. Zbl 1426.14016
Bürgisser, Peter; Cucker, Felipe; Lairez, Pierre
2
2019
On flocks under switching directed interaction topologies. Zbl 1405.93014
Cucker, Felipe; Dong, Jiu-Gang
2
2019
A stable, polynomial-time algorithm for the eigenpair problem. Zbl 1401.65034
Armentano, Diego; Beltrán, Carlos; Bürgisser, Peter; Cucker, Felipe; Shub, Michael
3
2018
Computing the homology of real projective sets. Zbl 07031361
Cucker, Felipe; Krick, Teresa; Shub, Michael
1
2018
On the condition of the zeros of characteristic polynomials. Zbl 1372.65103
Bürgisser, Peter; Cucker, Felipe; Rocha Cardozo, Elisa
1
2017
On flocks influenced by closest neighbors. Zbl 1354.93069
Cucker, Felipe; Dong, Jiu-Gang
11
2016
Condition length and complexity for the solution of polynomial systems. Zbl 1358.65031
Armentano, Diego; Beltrán, Carlos; Bürgisser, Peter; Cucker, Felipe; Shub, Michael
4
2016
A randomized homotopy for the Hermitian eigenpair problem. Zbl 1317.65096
Armentano, Diego; Cucker, Felipe
2
2015
Solving second-order conic systems with variable precision. Zbl 1309.90076
Cucker, Felipe; Peña, Javier; Roshchina, Vera
2
2015
A theory of complexity, condition, and roundoff. Zbl 1307.68037
Cucker, Felipe
2
2015
Smoothed analysis of componentwise condition numbers for sparse matrices. Zbl 1323.65045
Cheung, Dennis; Cucker, Felipe
1
2015
A conditional, collision-avoiding, model for swarming. Zbl 1273.93087
Cucker, Felipe; Dong, Jiu-Gang
7
2014
Fast computation of zeros of polynomial systems with bounded degree under finite-precision. Zbl 1291.65158
Briquel, Irénée; Cucker, Felipe; Peña, Javier; Roshchina, Vera
4
2014
Condition. The geometry of numerical algorithms. Zbl 1280.65041
Bürgisser, Peter; Cucker, Felipe
37
2013
On the average condition of random linear programs. Zbl 1273.90116
Cheung, Dennis; Cucker, Felipe
1
2013
Manifold mirrors. The crossing paths of the arts and mathematics. Zbl 1300.00023
Cucker, Felipe
1
2013
A numerical algorithm for zero counting. III: Randomization and condition. Zbl 1245.65189
Cucker, Felipe; Krick, Teresa; Malajovich, Gregorio; Wschebor, Mario
9
2012
The legacy of Turing in numerical analysis. Zbl 1274.01074
Cucker, Felipe
1
2012
A general collision-avoiding flocking framework. Zbl 1368.93261
Cucker, Felipe; Dong, Jiu-Gang
28
2011
On a problem posed by Steve Smale. Zbl 1248.65047
Bürgisser, Peter; Cucker, Felipe
22
2011
Systems of polynomial equations. Zbl 1361.65031
Cucker, Felipe; Malajovich, Gregorio
1
2011
Avoiding collisions in flocks. Zbl 1368.93370
Cucker, Felipe; Dong, Jiu-Gang
54
2010
Coverage processes on spheres and condition numbers for linear programming. Zbl 1205.60027
Bürgisser, Peter; Cucker, Felipe; Lotz, Martin
9
2010
Smoothed analysis of Moore-Penrose inversion. Zbl 1227.65035
Bürgisser, Peter; Cucker, Felipe
4
2010
Adversarial smoothed analysis. Zbl 1232.65071
Cucker, Felipe; Hauser, Raphael; Lotz, Martin
2
2010
On strata of degenerate polyhedral cones. II: Relations between condition measures. Zbl 1273.90214
Cheung, Dennis; Cucker, Felipe; Peña, Javier
1
2010
On the critical exponent for flocks under hierarchical leadership. Zbl 1202.92089
Cucker, Felipe; Dong, Jiu-Gang
27
2009
A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysis. Zbl 1215.65218
Cucker, Felipe; Krick, Teresa; Malajovich, Gregorio; Wschebor, Mario
10
2009
Exotic quantifiers, complexity classes, and complete problems. Zbl 1185.68343
Bürgisser, Peter; Cucker, Felipe
7
2009
On strata of degenerate polyhedral cones. I: Condition and distance to strata. Zbl 1163.90644
Cheung, Dennis; Cucker, Felipe; Peña, Javier
3
2009
Foundations of computational mathematics, Hong Kong, China, 2008. Selected papers based on the presentations at the international conference of the Society for the Foundations of Computational Mathematics (FoCM), June 16–26, 2008. Zbl 1170.13001
Cucker, Felipe (ed.); Pinkus, Allan (ed.); Todd, Michael J. (ed.)
1
2009
Flocking in noisy environments. Zbl 1273.91404
Cucker, Felipe; Mordecki, Ernesto
70
2008
Flocking with informed agents. Zbl 1163.93306
Cucker, Felipe; Huepe, Cristián
27
2008
The probability that a slightly perturbed numerical analysis problem is difficult. Zbl 1195.65018
Bürgisser, Peter; Cucker, Felipe; Lotz, Martin
14
2008
A numerical algorithm for zero counting. I: Complexity and accuracy. Zbl 1166.65021
Cucker, Felipe; Krick, Teresa; Malajovich, Gregorio; Wschebor, Mario
11
2008
A condition number for multifold conic systems. Zbl 1168.90572
Cheung, Dennis; Cucker, Felipe; Peña, Javier
3
2008
Emergent behavior in flocks. Zbl 1366.91116
Cucker, Felipe; Smale, Steve
342
2007
Learning theory. An approximation theory viewpoint. Zbl 1274.41001
Cucker, Felipe; Zhou, Ding Xuan
196
2007
On the mathematics of emergence. Zbl 1166.92323
Cucker, Felipe; Smale, Steve
106
2007
On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems. Zbl 1115.15004
Cucker, Felipe; Diao, Huaian; Wei, Yimin
39
2007
Mixed and componentwise condition numbers for rectangular structured matrices. Zbl 1168.15304
Cucker, Felipe; Diao, Huaian
10
2007
A note on parallel and alternating time. Zbl 1137.65076
Cucker, Felipe; Briquel, Irénée
2
2007
Counting complexity classes for numeric computations. II: Algebraic and semialgebraic sets. Zbl 1149.68029
Bürgisser, Peter; Cucker, Felipe
16
2006
Smoothed analysis of complex conic condition numbers. Zbl 1113.65044
Bürgisser, Peter; Cucker, Felipe; Lotz, Martin
12
2006
Smoothed analysis of some condition numbers. Zbl 1198.65084
Cucker, F.; Diao, H.; Wei, Y.
12
2006
Solving linear programs with finite precision. II: Algorithms. Zbl 1105.90042
Cheung, Dennis; Cucker, Felipe
8
2006
The complexity of semilinear problems in succinct representation. Zbl 1113.68057
Bürgisser, Peter; Cucker, Felipe; de Naurois, Paulin Jacobé
4
2006
General formulas for the smoothed analysis of condition numbers. Zbl 1121.65041
Bürgisser, Peter; Cucker, Felipe; Lotz, Martin
3
2006
Implicit complexity over an arbitrary structure: Quantifier alternations. Zbl 1093.68041
Bournez, Olivier; Cucker, Felipe; de Naurois, Paulin Jacobé; Marion, Jean-Yves
2
2006
Counting complexity classes for numeric computations. III: Complex projective sets. Zbl 1100.68032
Bürgisser, Peter; Cucker, Felipe; Lotz, Martin
6
2005
A note on level-2 condition numbers. Zbl 1074.15008
Cheung, Dennis; Cucker, Felipe
6
2005
Tail decay and moment estimates of a condition number for random linear conic systems. Zbl 1097.90057
Cheung, Dennis; Cucker, Felipe; Hauser, Raphael
4
2005
Implicit complexity over an arbitrary structure: sequential and parallel polynomial time. Zbl 1077.03021
Bounez, Olivier; Cucker, Felipe; Jacobé de Naurois, Paulin; Marion, Jean-Yves
3
2005
Modeling language evolution. Zbl 1083.68131
Cucker, Felipe; Smale, Steve; Zhou, Ding-Xuan
15
2004
Variations by complexity theorists on three themes of Euler, Bézout, Betti, and Poincaré. Zbl 1076.68033
Bürgisser, Peter; Cucker, Felipe
8
2004
Solving linear programs with finite precision. I: Condition numbers and random programs. Zbl 1082.90060
Cheung, Dennis; Cucker, Felipe
7
2004
Counting complexity classes for numeric computations. II. Algebraic and semialgebraic sets. Zbl 1192.68289
Bürgisser, Peter; Cucker, Felipe
2
2004
Unifying condition numbers for linear programming. Zbl 1082.90061
Cheung, Dennis; Cucker, Felipe; Peña, Javier
12
2003
On the expected condition number of linear programming problems. Zbl 1030.65039
Cucker, Felipe; Wschebor, Mario
11
2003
Computability over an arbitrary structure. Sequential and parallel polynomial time. Zbl 1029.68056
Bournez, Olivier; Cucker, Felipe; de Naurois, Paulin Jacobé; Marion, Jean-Yves
8
2003
Counting complexity classes for numeric computations. I: Semilinear sets. Zbl 1069.68049
Bürgisser, Peter; Cucker, Felipe
4
2003
Safe recursion over an arbitrary structure: PAR, PH and DPH. Zbl 1261.68058
Bournez, Olivier; Cucker, Felipe; De Naurois, Paulin Jacobé; Marion, Jean-Yves
1
2003
Linear programming and condition numbers under the real number computation model. Zbl 1070.65548
Cheung, Dennis; Cucker, Filipe; Ye, Yinyu
1
2003
On the mathematical foundations of learning. Zbl 0983.68162
Cucker, Felipe; Smale, Steve
322
2002
Best choices for regularization parameters in learning theory: on the bias-variance problem. Zbl 1057.68085
Cucker, Felipe; Smale, Steve
78
2002
Probabilistic analysis of condition numbers for linear programming. Zbl 1041.90028
Cheung, D.; Cucker, F.
6
2002
The work of Steve Smale on the theory of computation: 1990-1999. Zbl 1050.68042
Cucker, Felipe; Blum, Lenore
3
2002
Real computations with fake numbers. Zbl 1004.68069
Cucker, Felipe
2
2002
A new condition number for linear programming. Zbl 1072.90564
Cheung, Dennis; Cucker, Felipe
21
2001
A primal-dual algorithm for solving polyhedral conic systems with a finite-precision machine. Zbl 0996.90052
Cucker, Felipe; Peña, Javier
16
2001
There are no sparse NP\(_{w}\)-hard sets. Zbl 0992.68061
Cucker, Felipe; Grigoriev, Dima
2
2001
On weak and weighted computations over the real closure of \(\mathbb{Q}\). Zbl 0977.68034
Cucker, Felipe
1
2001
Complexity estimates depending on condition and round-off error. Zbl 1065.68533
Cucker, Felipe; Smale, Steve
19
1999
A polynomial time algorithm for diophantine equations in one variable. Zbl 0920.11085
Cucker, Felipe; Koiran, Pascal; Smale, Steve
11
1999
Approximate zeros and condition numbers. Zbl 0967.65063
Cucker, Felipe
6
1999
Logics which capture complexity classes over the reals. Zbl 0933.03047
Cucker, Felipe; Meer, Klaus
5
1999
Real computations with fake numbers. Zbl 0944.03030
Cucker, Felipe
2
1999
Complexity lower bounds for approximation algebraic computation trees. Zbl 0959.68143
Cucker, Felipe; Grigoriev, Dima
1
1999
Complexity and real computation. Foreword by Richard M. Karp. Zbl 0948.68068
Blum, Leonore; Cucker, Felipe; Shub, Michael; Smale, Steve
53
1997
On the power of real Turing machines over binary inputs. Zbl 0874.68110
Cucker, Felipe; Grigoriev, Dima
14
1997
Complexity and dimension. Zbl 1337.68117
Cucker, Felipe; Koiran, Pascal; Matamala, Martín
4
1997
Machines over the reals and non-uniformity. Zbl 0941.03038
Cucker, Felipe
1
1997
Complexity and real computation: A manifesto. Zbl 0872.68036
Blum, Lenore; Cucker, Felipe; Shub, Mike; Smale, Steve
282
1996
Algebraic settings for the problem ”P\(\neq\)NP?”. Zbl 0856.68068
Blum, Lenore; Cucker, Felipe; Shub, Mike; Smale, Steve
12
1996
On digital nondeterminism. Zbl 0868.68058
Cucker, F.; Matamala, M.
10
1996
Generalized Knapsack problems and fixed degree separations. Zbl 0900.68212
Cucker, Felipe; Shub, Michael
3
1996
Computing over the reals with addition and order: Higher complexity classes. Zbl 0843.68033
Cucker, Felipe; Koiran, Pascal
16
1995
On real Turing machines that toss coins. Zbl 0938.68648
Cucker, Felipe; Karpinski, Marek; Koiran, Pascal; Lickteig, Thomas; Werther, Kai
9
1995
Models for parallel computation with real numbers. Zbl 0921.68056
Cucker, F.; Montaña, J. L.; Pardo, L. M.
1
1995
Separation of complexity classes in Koiran’s weak model. Zbl 0819.68053
Cucker, F.; Shub, M.; Smale, S.
15
1994
On the complexity of quantifier elimination: The structural approach. Zbl 0788.68058
Cucker, Felipe
13
1993
\(P_ \mathbb{R}{}\neq{}NC_ \mathbb{R}\). Zbl 0753.68044
Cucker, Felipe
9
1992
Two \(P\)-complete problems in the theory of the reals. Zbl 0759.68032
Cucker, F.; Torrecillas, A.
7
1992
The arithmetical hierarchy over the reals. Zbl 0765.03020
Cucker, Felipe
5
1992
Time bounded computations over the reals. Zbl 0788.68043
Cucker, F.; Montaña, J. L.; Pardo, L. M.
3
1992
NC algorithms for real algebraic numbers. Zbl 0786.12007
Cucker, F.; Lanneau, H.; Mishra, B.; Pedersen, P.; Roy, M.-F.
2
1992
On algorithms for real algebraic plane curves. Zbl 0737.14017
Cucker, Felipe; González-Vega, Laureano; Rossello, Francesc
10
1991
Two P-complete problems in the theory of the reals. Zbl 0785.68038
Cucker, F.; Torrecillas, A.
2
1991
A theorem on random polynomials and some consequences in average complexity. Zbl 0725.12007
Cucker, F.; Roy, M.-F.
2
1990
An alternate proof of the continuity of the roots of a polynomial. Zbl 0708.30010
Cucker, Felipe; Corbalan, Antonio Gonzalez
12
1989
...and 5 more Documents
all top 5

Cited by 1,680 Authors

66 Ha, Seung-Yeal
58 Cucker, Felipe
31 Zhou, Dingxuan
23 Choi, Young-Pil
22 Carrillo de la Plata, José Antonio
21 Chen, Dirong
20 Bürgisser, Peter
20 Sun, Hongwei
19 Meer, Klaus
18 Sheng, Baohuai
17 Pardo, Luis Miguel
17 Wei, Yimin
16 Degond, Pierre
16 Kim, Jeongho
16 Koiran, Pascal
15 Bellomo, Nicola
15 Beltrán, Carlos
15 Li, Luoqing
15 Pillonetto, Gianluigi
15 Xiang, Dao-Hong
14 Peña, Javier F.
14 Shub, Michael
14 Wu, Qiang
13 Chen, Hong
13 Smale, Steve
13 Xu, Zongben
12 Fornasier, Massimo
12 Guo, Zheng-Chu
12 Zhang, Xiongtao
11 Diao, Huaian
11 Dong, Jiu-Gang
11 Ko, Dongnam
11 Rosasco, Lorenzo A.
11 Sanguineti, Marcello
11 Tong, Hongzhi
10 Cao, Feilong
10 Li, Zhuchun
10 Lotz, Martin
10 Malajovich, Gregorio
10 Zhang, Haizhang
10 Zou, Bin
9 Dedieu, Jean-Pierre
9 Feng, Yunlong
9 Ferreira, Orizon Pereira
9 Kim, Doheon
9 Lv, Shaogao
9 Peszek, Jan
9 Shi, Lei
9 Tan, Changhui
8 Armentano, Diego
8 Bae, Hyeong-Ohk
8 Basu, Saugata
8 Gnecco, Giorgio
8 Kang, Moon-Jin
8 Kim, Dohyun
8 Li, Chong
8 Rojas, J. Maurice
8 Tadmor, Eitan
7 Cai, Jia
7 De Vito, Ernesto
7 Haskovec, Jan
7 Li, Hanyu
7 Lin, Shaobo
7 Malinowska, Agnieszka Barbara
7 Menegatto, Valdir Antonio
7 Piccoli, Benedetto
7 Verschelde, Jan
7 Yakoubsohn, Jean-Claude
7 Ye, Peixin
7 Ying, Yiming
7 Ziegler, Martin
6 Bongini, Mattia
6 Breiding, Paul
6 Brezzi, Franco
6 Cheung, Dennis
6 Hauenstein, Jonathan D.
6 Matera, Guillermo
6 Motsch, Sébastien
6 Odzijewicz, Tatiana
6 Qiao, Sanzheng
6 Roshchina, Vera
6 Shvydkoy, Roman V.
6 Steinwart, Ingo
6 Suykens, Johan A. K.
6 Wang, Jianli
6 Wang, Shaoxin
6 Wschebor, Mario
6 Wu, Wenyuan
6 Xue, Xiaoping
6 Zhang, Yongquan
5 Cánovas, María Josefa
5 Caponnetto, Andrea
5 Chen, Heng
5 Christmann, Andreas
5 Finkel, Olivier
5 Gaßner, Christine
5 Giusti, Marc
5 Guo, Lei
5 Guo, Xin
5 Heintz, Joos
...and 1,580 more Authors
all top 5

Cited in 308 Serials

109 Journal of Complexity
64 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
49 Theoretical Computer Science
44 Foundations of Computational Mathematics
32 Automatica
30 Journal of Symbolic Computation
30 Neural Computation
29 Analysis and Applications (Singapore)
25 International Journal of Wavelets, Multiresolution and Information Processing
23 Applied and Computational Harmonic Analysis
21 Journal of Computational and Applied Mathematics
18 Journal of Mathematical Analysis and Applications
16 Advances in Computational Mathematics
16 Kinetic and Related Models
14 Journal of Statistical Physics
14 Mathematics of Computation
14 Journal of Differential Equations
14 Neural Networks
14 Mathematical Programming. Series A. Series B
13 Applied Mathematics and Computation
13 Journal of Approximation Theory
12 Systems & Control Letters
12 Abstract and Applied Analysis
11 Linear Algebra and its Applications
11 SIAM Journal on Mathematical Analysis
11 Theory of Computing Systems
11 Networks and Heterogeneous Media
10 Archive for Rational Mechanics and Analysis
10 Computers & Mathematics with Applications
10 Information Processing Letters
10 Physica D
10 Applied Mathematics Letters
10 Discrete and Continuous Dynamical Systems
10 Journal of Machine Learning Research (JMLR)
9 Journal of the Franklin Institute
9 The Annals of Statistics
9 Journal of Multivariate Analysis
9 Acta Mathematica Sinica. English Series
8 Journal of Mathematical Physics
8 Journal of Statistical Planning and Inference
8 SIAM Journal on Control and Optimization
8 Constructive Approximation
8 SIAM Journal on Optimization
8 Mathematical Logic Quarterly (MLQ)
8 Journal of Systems Science and Complexity
7 Information Sciences
7 Information and Computation
7 Machine Learning
7 SIAM Journal on Applied Mathematics
7 Discrete and Continuous Dynamical Systems. Series B
7 Comptes Rendus. Mathématique. Académie des Sciences, Paris
7 Science China. Mathematics
6 International Journal of Control
6 Nonlinearity
6 Journal of Optimization Theory and Applications
6 The Annals of Applied Probability
6 Applicable Algebra in Engineering, Communication and Computing
6 Computational Complexity
6 Numerical Linear Algebra with Applications
5 Applicable Analysis
5 Journal of Pure and Applied Algebra
5 Quarterly of Applied Mathematics
5 SIAM Journal on Numerical Analysis
5 Annals of Pure and Applied Logic
5 Optimization
5 Numerical Algorithms
5 International Journal of Computer Mathematics
5 Frontiers of Mathematics in China
5 Journal of Theoretical Biology
4 Discrete Applied Mathematics
4 Calcolo
4 Journal of Computer and System Sciences
4 Numerical Functional Analysis and Optimization
4 SIAM Journal on Computing
4 Discrete & Computational Geometry
4 Journal of Global Optimization
4 Optimization Methods & Software
4 Chaos
4 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
4 Communications on Pure and Applied Analysis
4 SIAM Journal on Applied Dynamical Systems
4 Electronic Journal of Statistics
3 Inverse Problems
3 Israel Journal of Mathematics
3 Journal of Mathematical Biology
3 Mathematical Notes
3 Physics Letters. A
3 Bulletin of Mathematical Biology
3 Journal of Functional Analysis
3 Numerische Mathematik
3 Proceedings of the American Mathematical Society
3 Transactions of the American Mathematical Society
3 Journal of the American Mathematical Society
3 Mathematical and Computer Modelling
3 SIAM Journal on Matrix Analysis and Applications
3 Journal of Integral Equations and Applications
3 Applied Mathematical Modelling
3 Chinese Science Bulletin
3 International Journal of Robust and Nonlinear Control
3 Experimental Mathematics
...and 208 more Serials
all top 5

Cited in 58 Fields

580 Computer science (68-XX)
288 Numerical analysis (65-XX)
215 Statistics (62-XX)
170 Biology and other natural sciences (92-XX)
143 Partial differential equations (35-XX)
136 Systems theory; control (93-XX)
106 Operations research, mathematical programming (90-XX)
102 Probability theory and stochastic processes (60-XX)
87 Mathematical logic and foundations (03-XX)
86 Statistical mechanics, structure of matter (82-XX)
79 Algebraic geometry (14-XX)
79 Functional analysis (46-XX)
76 Ordinary differential equations (34-XX)
75 Linear and multilinear algebra; matrix theory (15-XX)
71 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
68 Approximations and expansions (41-XX)
54 Field theory and polynomials (12-XX)
54 Dynamical systems and ergodic theory (37-XX)
48 Calculus of variations and optimal control; optimization (49-XX)
42 Information and communication theory, circuits (94-XX)
35 Functions of a complex variable (30-XX)
35 Harmonic analysis on Euclidean spaces (42-XX)
33 Operator theory (47-XX)
32 Real functions (26-XX)
31 Fluid mechanics (76-XX)
25 Number theory (11-XX)
24 Combinatorics (05-XX)
22 Mechanics of particles and systems (70-XX)
20 Commutative algebra (13-XX)
20 Convex and discrete geometry (52-XX)
14 Difference and functional equations (39-XX)
14 Integral equations (45-XX)
13 Global analysis, analysis on manifolds (58-XX)
11 Differential geometry (53-XX)
10 General and overarching topics; collections (00-XX)
9 History and biography (01-XX)
9 Mechanics of deformable solids (74-XX)
9 Quantum theory (81-XX)
7 Several complex variables and analytic spaces (32-XX)
7 Abstract harmonic analysis (43-XX)
5 Measure and integration (28-XX)
5 Special functions (33-XX)
4 Group theory and generalizations (20-XX)
4 Potential theory (31-XX)
4 General topology (54-XX)
3 Associative rings and algebras (16-XX)
3 Topological groups, Lie groups (22-XX)
3 Geometry (51-XX)
3 Algebraic topology (55-XX)
3 Manifolds and cell complexes (57-XX)
2 Integral transforms, operational calculus (44-XX)
2 Optics, electromagnetic theory (78-XX)
1 Order, lattices, ordered algebraic structures (06-XX)
1 General algebraic systems (08-XX)
1 Category theory; homological algebra (18-XX)
1 Classical thermodynamics, heat transfer (80-XX)
1 Relativity and gravitational theory (83-XX)
1 Mathematics education (97-XX)

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