# zbMATH — the first resource for mathematics

## Cucker, Felipe

Compute Distance To:
 Author ID: 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

#### Co-Authors

 27 single-authored 24 Bürgisser, Peter 15 Cheung, Dennis 12 Smale, Steve 10 Shub, Michael 8 de Naurois, Paulin Jacobé 8 Peña, Javier F. 7 Lotz, Martin 6 Dong, Jiu-Gang 6 Krick, Teresa 5 Blum, Lenore 5 Bournez, Olivier 5 Marion, Jean-Yves 4 Grigor’ev, Dmitriĭ Yur’evich 4 Koiran, Pascal 4 Malajovich, Gregorio 4 Pardo, Luis Miguel 4 Roy, Marie-Françoise 4 Wschebor, Mario 3 Armentano, Diego 3 Diao, Huaian 3 Montaña, José Luis 3 Roshchina, Vera 2 Beltrán, Carlos 2 Briquel, Irénée 2 Hauser, Raphael Andreas 2 Lickteig, Thomas 2 Matamala, Martín 2 Pinkus, Allan M. 2 Rosselló, Francesc 2 Tonelli-Cueto, Josué 2 Torrecillas, A. 2 Wei, Yimin 2 Zhou, Dingxuan 1 Castro, Jocelyn A. 1 Corbalan, Antonio Gonzalez 1 Dedieu, Jean-Piere 1 DeVore, Ronald A. 1 Ergür, Alperen Ali 1 Gabarró, Joaquim 1 Gonzalez-Vega, Laureano 1 Huepe, Cristián 1 Karpinski, Marek 1 Lairez, Pierre 1 Lanneau, H. 1 Meer, Klaus 1 Mishra, Bhavya 1 Mordecki, Ernesto 1 Olver, Peter John 1 Pedersen, Poul Wulff 1 Raimondo, Mario 1 Recio, Tomas 1 Rocha Cardozo, Elisa 1 Rojas, J. Maurice 1 Süli, Endre E. 1 Szántó, Ágnes 1 Todd, Michael J. 1 Werther, Kai 1 Ye, Yinyu
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
all top 5

#### Fields

 76 Computer science (68-XX) 50 Numerical analysis (65-XX) 24 Mathematical logic and foundations (03-XX) 20 Algebraic geometry (14-XX) 19 Operations research, mathematical programming (90-XX) 15 Linear and multilinear algebra; matrix theory (15-XX) 10 General and overarching topics; collections (00-XX) 8 Field theory and polynomials (12-XX) 7 Systems theory; control (93-XX) 5 Functions of a complex variable (30-XX) 4 Number theory (11-XX) 4 Commutative algebra (13-XX) 4 Real functions (26-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Biology and other natural sciences (92-XX) 3 Ordinary differential equations (34-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Convex and discrete geometry (52-XX) 3 Algebraic topology (55-XX) 3 Probability theory and stochastic processes (60-XX) 3 Statistics (62-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Differential geometry (53-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Category theory; homological algebra (18-XX) 1 Group theory and generalizations (20-XX) 1 Approximations and expansions (41-XX) 1 Geometry (51-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX) 1 Statistical mechanics, structure of matter (82-XX)

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

#### Wikidata Timeline

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.