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2020 – today
- 2023
[i15]Alexander Bastounis, Felipe Cucker, Anders C. Hansen:
When can you trust feature selection? - I: A condition-based analysis of LASSO and generalised hardness of approximation. CoRR abs/2312.11425 (2023)- 2022
- [j76]Felipe Cucker, Alperen Ali Ergür
, Josué Tonelli-Cueto:
On the Complexity of the Plantinga-Vegter Algorithm. Discret. Comput. Geom. 68(3): 664-708 (2022) - 2021
- [j75]Peter Bürgisser, Felipe Cucker, Josué Tonelli-Cueto:
Computing the Homology of Semialgebraic Sets. II: General Formulas. Found. Comput. Math. 21(5): 1279-1316 (2021) - [i14]Felipe Cucker, Alperen Ali Ergür, Josué Tonelli-Cueto:
Functional norms, condition numbers and numerical algorithms in algebraic geometry. CoRR abs/2102.11727 (2021) - 2020
- [j74]Peter Bürgisser, Felipe Cucker, Josué Tonelli-Cueto:
Computing the Homology of Semialgebraic Sets. I: Lax Formulas. Found. Comput. Math. 20(1): 71-118 (2020) - [j73]Felipe Cucker, Teresa Krick:
On local analysis. J. Complex. 57: 101442 (2020) - [i13]Felipe Cucker, Alperen Ali Ergür, Josué Tonelli-Cueto:
On the Complexity of the Plantinga-Vegter Algorithm. CoRR abs/2004.06879 (2020) - [i12]Peter Bürgisser, Felipe Cucker, Pierre Lairez:
Rigid continuation paths II. Structured polynomial systems. CoRR abs/2010.10997 (2020)
2010 – 2019
- 2019
- [j72]Peter Bürgisser, Felipe Cucker, Pierre Lairez:
Computing the Homology of Basic Semialgebraic Sets in Weak Exponential Time. J. ACM 66(1): 5:1-5:30 (2019) - [j71]Felipe Cucker, Jiu-Gang Dong:
On Flocks Under Switching Directed Interaction Topologies. SIAM J. Appl. Math. 79(1): 95-110 (2019) - [c22]Felipe Cucker:
Recent Advances in the Computation of the Homology of Semialgebraic Sets. CiE 2019: 1-12 - [c21]Felipe Cucker, Alperen Ali Ergür, Josué Tonelli-Cueto:
Plantinga-Vegter Algorithm takes Average Polynomial Time. ISSAC 2019: 114-121 - [i11]Felipe Cucker, Alperen Ali Ergür, Josué Tonelli-Cueto:
Plantinga-Vegter algorithm takes average polynomial time. CoRR abs/1901.09234 (2019) - [i10]Peter Bürgisser, Felipe Cucker, Josué Tonelli-Cueto:
Computing the Homology of Semialgebraic Sets. II: General formulas. CoRR abs/1903.10710 (2019) - 2018
- [j70]Felipe Cucker, Teresa Krick, Michael Shub:
Computing the Homology of Real Projective Sets. Found. Comput. Math. 18(4): 929-970 (2018) - [i9]Peter Bürgisser, Felipe Cucker, Josué Tonelli-Cueto:
Computing the Homology of Semialgebraic Sets I: Lax Formulas. CoRR abs/1807.06435 (2018) - 2017
- [j69]Peter Bürgisser, Felipe Cucker, Elisa Rocha Cardozo:
On the condition of the zeros of characteristic polynomials. J. Complex. 42: 72-84 (2017) - [i8]Felipe Cucker, Peter Bürgisser, Pierre Lairez:
Computing the homology of basic semialgebraic sets in weak exponential time. CoRR abs/1706.07473 (2017) - 2016
- [j68]Felipe Cucker:
Probabilistic analyses of condition numbers. Acta Numer. 25: 321-382 (2016) - [j67]Diego Armentano, Carlos Beltrán, Peter Bürgisser, Felipe Cucker, Michael Shub:
Condition Length and Complexity for the Solution of Polynomial Systems. Found. Comput. Math. 16(6): 1401-1422 (2016) - 2015
- [j66]Diego Armentano, Felipe Cucker:
A Randomized Homotopy for the Hermitian Eigenpair Problem. Found. Comput. Math. 15(1): 281-312 (2015) - [j65]Felipe Cucker, Javier Peña, Vera Roshchina:
Solving second-order conic systems with variable precision. Math. Program. 150(2): 217-250 (2015) - [i7]Peter Bürgisser, Felipe Cucker, Marek Karpinski, Nicolai N. Vorobjov Jr.:
Complexity of Symbolic and Numerical Problems (Dagstuhl Seminar 15242). Dagstuhl Reports 5(6): 28-47 (2015) - 2014
- [j64]Irénée Briquel, Felipe Cucker, Javier Peña, Vera Roshchina:
Fast computation of zeros of polynomial systems with bounded degree under finite-precision. Math. Comput. 83(287): 1279-1317 (2014) - [i6]Felipe Cucker:
A Theory of Complexity, Condition and Roundoff. CoRR abs/1403.6241 (2014) - 2013
- [b1]Peter Bürgisser, Felipe Cucker:
Condition - The Geometry of Numerical Algorithms. Grundlehren der mathematischen Wissenschaften 349, Springer 2013, ISBN 978-3-642-38895-8, pp. I-XXXI, 1-554 - [j63]Dennis Cheung, Felipe Cucker:
On the Average Condition of Random Linear Programs. SIAM J. Optim. 23(2): 799-810 (2013) - 2012
- [j62]Felipe Cucker, Teresa Krick, Gregorio Malajovich, Mario Wschebor:
A numerical algorithm for zero counting. III: Randomization and condition. Adv. Appl. Math. 48(1): 215-248 (2012) - [c20]Felipe Cucker:
The Legacy of Turing in Numerical Analysis. SOFSEM 2012: 1-13 - 2011
- [j61]Felipe Cucker, Jiu-Gang Dong:
A General Collision-Avoiding Flocking Framework. IEEE Trans. Autom. Control. 56(5): 1124-1129 (2011) - 2010
- [j60]Dennis Cheung, Felipe Cucker, Javier Peña:
On strata of degenerate polyhedral cones, II: Relations between condition measures. J. Complex. 26(2): 209-226 (2010) - [j59]Felipe Cucker, Raphael A. Hauser, Martin Lotz:
Adversarial smoothed analysis. J. Complex. 26(3): 255-262 (2010) - [j58]Peter Bürgisser, Felipe Cucker:
Smoothed Analysis of Moore-Penrose Inversion. SIAM J. Matrix Anal. Appl. 31(5): 2769-2783 (2010) - [j57]Felipe Cucker, Jiu-Gang Dong:
Avoiding Collisions in Flocks. IEEE Trans. Autom. Control. 55(5): 1238-1243 (2010) - [c19]Peter Bürgisser, Felipe Cucker:
Solving polynomial equations in smoothed polynomial time and a near solution to smale's 17th problem. STOC 2010: 503-512 - [i5]Felipe Cucker, Teresa Krick, Gregorio Malajovich, Mario Wschebor:
A Numerical Algorithm for Zero Counting. III: Randomization and Condition. CoRR abs/1007.1597 (2010)
2000 – 2009
- 2009
- [j56]Felipe Cucker, Paulin Jacobé de Naurois:
Parallel Time and Quantifier Prefixes. Comput. Complex. 18(4): 527-550 (2009) - [j55]Dennis Cheung, Felipe Cucker, Javier Peña:
On strata of degenerate polyhedral cones I: Condition and distance to strata. Eur. J. Oper. Res. 198(1): 23-28 (2009) - [j54]Peter Bürgisser, Felipe Cucker:
Exotic Quantifiers, Complexity Classes, and Complete Problems. Found. Comput. Math. 9(2): 135-170 (2009) - [j53]Dennis Cheung, Felipe Cucker:
Componentwise Condition Numbers of Random Sparse Matrices. SIAM J. Matrix Anal. Appl. 31(2): 721-731 (2009) - [i4]Felipe Cucker, Teresa Krick, Gregorio Malajovich, Mario Wschebor:
A Numerical Algorithm for Zero Counting. II: Distance to Ill-posedness and Smoothed Analysis. CoRR abs/0909.4101 (2009) - 2008
- [j52]Felipe Cucker, Teresa Krick, Gregorio Malajovich, Mario Wschebor:
A numerical algorithm for zero counting, I: Complexity and accuracy. J. Complex. 24(5-6): 582-605 (2008) - [j51]Peter Bürgisser, Felipe Cucker, Martin Lotz:
The probability that a slightly perturbed numerical analysis problem is difficult. Math. Comput. 77(263): 1559-1583 (2008) - [j50]Dennis Cheung, Felipe Cucker, Javier Peña:
A Condition Number for Multifold Conic Systems. SIAM J. Optim. 19(1): 261-280 (2008) - 2007
- [j49]Felipe Cucker, Irénée Briquel:
A note on parallel and alternating time. J. Complex. 23(4-6): 594-602 (2007) - [j48]Felipe Cucker, Huaian Diao, Yimin Wei:
On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems. Math. Comput. 76(258): 947-963 (2007) - [j47]Felipe Cucker, Steve Smale:
Emergent Behavior in Flocks. IEEE Trans. Autom. Control. 52(5): 852-862 (2007) - [c18]Peter Bürgisser, Felipe Cucker:
Exotic Quantifiers, Complexity Classes, and Complete Problems. ICALP 2007: 207-218 - [i3]Felipe Cucker, Teresa Krick, Gregorio Malajovich, Mario Wschebor:
A Numerical Algorithm for Zero Counting. I: Complexity and Accuracy. CoRR abs/0710.4508 (2007) - 2006
- [j46]Peter Bürgisser, Felipe Cucker, Paulin Jacobé de Naurois:
The complexity of semilinear problems in succinct representation. Comput. Complex. 15(3): 197-235 (2006) - [j45]Olivier Bournez, Felipe Cucker, Paulin Jacobé de Naurois, Jean-Yves Marion:
Implicit complexity over an arbitrary structure: Quantifier alternations. Inf. Comput. 204(2): 210-230 (2006) - [j44]Peter Bürgisser, Felipe Cucker:
Counting complexity classes for numeric computations II: Algebraic and semialgebraic sets. J. Complex. 22(2): 147-191 (2006) - [j43]Dennis Cheung, Felipe Cucker:
Solving linear programs with finite precision: II. Algorithms. J. Complex. 22(3): 305-335 (2006) - [j42]Felipe Cucker, Huaian Diao, Yimin Wei:
Smoothed analysis of some condition numbers. Numer. Linear Algebra Appl. 13(1): 71-84 (2006) - 2005
- [j41]Felipe Cucker:
On sparseness, reducibilities, and complexity. Ann. Pure Appl. Log. 134(1): 53-61 (2005) - [j40]Lenore Blum, Felipe Cucker, Tomaso A. Poggio, James Renegar, Michael Shub:
Foreword. Found. Comput. Math. 5(4): 349 (2005) - [j39]Peter Bürgisser, Felipe Cucker, Martin Lotz:
Counting Complexity Classes for Numeric Computations. III: Complex Projective Sets. Found. Comput. Math. 5(4): 351-387 (2005) - [j38]Dennis Cheung, Felipe Cucker:
A note on level-2 condition numbers. J. Complex. 21(3): 314-319 (2005) - [j37]Olivier Bournez, Felipe Cucker, Paulin Jacobé de Naurois, Jean-Yves Marion:
Implicit Complexity over an Arbitrary Structure: Sequential and Parallel Polynomial Time. J. Log. Comput. 15(1): 41-58 (2005) - [j36]Dennis Cheung, Felipe Cucker, Raphael A. Hauser:
Tail Decay and Moment Estimates of a Condition Number for Random Linear Conic Systems. SIAM J. Optim. 15(4): 1237-1261 (2005) - [c17]Peter Bürgisser, Felipe Cucker, Paulin Jacobé de Naurois:
The Complexity of Semilinear Problems in Succinct Representation. FCT 2005: 479-490 - [i2]Peter Bürgisser, Felipe Cucker:
Exotic quantifiers, complexity classes, and complete problems. Electron. Colloquium Comput. Complex. TR05 (2005) - 2004
- [j35]Felipe Cucker, Steve Smale, Ding-Xuan Zhou:
Modeling Language Evolution. Found. Comput. Math. 4(3): 315-343 (2004) - [j34]Dennis Cheung, Felipe Cucker:
Solving linear programs with finite precision: I. Condition numbers and random programs. Math. Program. 99(1): 175-196 (2004) - [c16]Olivier Bournez, Felipe Cucker, Paulin Jacobé de Naurois, Jean-Yves Marion:
Tailoring Recursion to Characterize Non-Deterministic Complexity Classes over Arbitrary Structures. IFIP TCS 2004: 409-422 - [c15]Peter Bürgisser, Felipe Cucker:
Counting complexity classes for numeric computations II: algebraic and semialgebraic sets. STOC 2004: 475-485 - 2003
- [j33]Dennis Cheung, Felipe Cucker:
Learning from rounded-off data. Inf. Comput. 182(1): 1-13 (2003) - [j32]Dennis Cheung, Felipe Cucker, Javier Peña:
Unifying Condition Numbers for Linear Programming. Math. Oper. Res. 28(4): 609-624 (2003) - [j31]Felipe Cucker, Mario Wschebor:
On the Expected Condition Number of Linear Programming Problems. Numerische Mathematik 94(3): 419-478 (2003) - [j30]Peter Bürgisser, Felipe Cucker:
Counting Complexity Classes for Numeric Computations I: Semilinear Sets. SIAM J. Comput. 33(1): 227-260 (2003) - [c14]Olivier Bournez, Felipe Cucker, Paulin Jacobé de Naurois, Jean-Yves Marion:
Computability over an Arbitrary Structure. Sequential and Parallel Polynomial Time. FoSSaCS 2003: 185-199 - [c13]Peter Bürgisser, Felipe Cucker:
Counting Complexity Classes over the Reals I: The Additive Case. ISAAC 2003: 625-634 - [c12]Olivier Bournez, Felipe Cucker, Paulin Jacobé de Naurois, Jean-Yves Marion:
Safe Recursion Over an Arbitrary Structure: PAR, PH and DPH. ICC@LICS 2003: 3-14 - [i1]Peter Bürgisser, Felipe Cucker:
Counting complexity classes for numeric computations II: algebraic and semialgebraic sets. CoRR cs.CC/0312007 (2003) - 2002
- [j29]Felipe Cucker, Steve Smale:
Best Choices for Regularization Parameters in Learning Theory: On the Bias-Variance Problem. Found. Comput. Math. 2(4): 413-428 (2002) - [j28]Felipe Cucker:
Real Computations with Fake Numbers. J. Complex. 18(1): 104-134 (2002) - [j27]Felipe Cucker, Javier Peña:
A Primal-Dual Algorithm for Solving Polyhedral Conic Systems with a Finite-Precision Machine. SIAM J. Optim. 12(2): 522-554 (2002) - [c11]Felipe Cucker:
On sparseness and Turing reducibility over the reals. WoLLIC 2002: 7-14 - 2001
- [j26]Dennis Cheung, Felipe Cucker:
A new condition number for linear programming. Math. Program. 91(1): 163-174 (2001) - [j25]Felipe Cucker, Dima Grigoriev:
There are No Sparse NPw-Hard Sets. SIAM J. Comput. 31(1): 193-198 (2001) - [j24]Felipe Cucker:
On weak and weighted computations over the real closure of Q. Theor. Comput. Sci. 255(1-2): 593-600 (2001) - [c10]Felipe Cucker, Dima Grigoriev:
There Are No Sparse NPW-Hard Sets. MFCS 2001: 285-291 - 2000
- [j23]Felipe Cucker, Thomas Lickteig:
Preface. J. Complex. 16(1): 1 (2000) - [c9]Felipe Cucker:
Solving polynomial systems: a complexity theory viewpoint. ISSAC 2000
1990 – 1999
- 1999
- [j22]Felipe Cucker, Steve Smale:
Complexity Estimates Depending on Condition and Round-Off Error. J. ACM 46(1): 113-184 (1999) - [j21]Felipe Cucker:
Approximate Zeros and Condition Numbers. J. Complex. 15(2): 214-226 (1999) - [j20]Felipe Cucker, Dima Grigoriev:
Complexity Lower Bounds for Approximation Algebraic Computation Trees. J. Complex. 15(4): 499-512 (1999) - [j19]Felipe Cucker, Pascal Koiran, Steve Smale:
A Polynomial Time Algorithm for Diophantine Equations in One Variable. J. Symb. Comput. 27(1): 21-29 (1999) - [j18]Felipe Cucker, Klaus Meer:
Logics Which Capture Complexity Classes Over The Reals. J. Symb. Log. 64(1): 363-390 (1999) - [c8]Felipe Cucker:
Real Computations with Fake Numbers. ICALP 1999: 55-73 - 1998
- [c7]Felipe Cucker, Steve Smale:
Complexity Estimates Depending on Condition and Round-Off Error. ESA 1998: 115-126 - 1997
- [j17]Felipe Cucker, Pascal Koiran, Martín Matamala:
Complexity and Dimension. Inf. Process. Lett. 62(4): 209-212 (1997) - [j16]Felipe Cucker:
Machines Over the Reals and Non Uniformity. Math. Log. Q. 43: 143-157 (1997) - [j15]Felipe Cucker, Dima Grigoriev:
On the Power of Real Turing Machines Over Binary Inputs. SIAM J. Comput. 26(1): 243-254 (1997) - [c6]Felipe Cucker, Klaus Meer:
Logics Which Capture Complexity Classes over the Reals. FCT 1997: 157-167 - 1996
- [j14]Felipe Cucker, Michael Shub:
EDITOR'S FOREWORD. J. Complex. 12(4): 255-256 (1996) - [j13]Felipe Cucker, Martín Matamala:
On Digital Nondeterminism. Math. Syst. Theory 29(6): 635-647 (1996) - [j12]Felipe Cucker, Mike Shub:
Generalized Knapsack Problems and Fixed Degree Separations. Theor. Comput. Sci. 161(1&2): 301-306 (1996) - 1995
- [j11]Felipe Cucker, Pascal Koiran:
Computing over the Reals with Addition and Order: Higher Complexity Classes. J. Complex. 11(3): 358-376 (1995) - [c5]Felipe Cucker, Marek Karpinski, Pascal Koiran, Thomas Lickteig, Kai Werther:
On real Turing machines that toss coins. STOC 1995: 335-342 - 1994
- [j10]Felipe Cucker, Mike Shub, Steve Smale:
Separation of Complexity Classes in Koiran's Weak Model. Theor. Comput. Sci. 133(1): 3-14 (1994) - 1993
- [j9]Felipe Cucker:
On the Complexity of Quantifier Elimination: the Structural Approach. Comput. J. 36(5): 400-408 (1993) - [c4]Felipe Cucker, Francesc Rosselló:
Recursiveness over the Complex Numbers is Time-Bounded. FSTTCS 1993: 260-267 - 1992
- [j8]Felipe Cucker, Hervé Lanneau, Bud Mishra, Paul Pedersen, Marie-Françoise Roy:
NC Algorithms for Real Algebraic Numbers. Appl. Algebra Eng. Commun. Comput. 3: 79-98 (1992) - [j7]Felipe Cucker, José L. Montaña, Luis M. Pardo:
Time Bounded Computations over the Reals. Int. J. Algebra Comput. 2(4): 395-408 (1992) - [j6]Felipe Cucker:
PR != NCR. J. Complex. 8(3): 230-238 (1992) - [j5]Felipe Cucker, A. Torrecillas:
Two P-complete problems in the theory of the reals. J. Complex. 8(4): 454-466 (1992) - [j4]Felipe Cucker:
The Arithmetical Hierarchy over the Reals. J. Log. Comput. 2(3): 375-395 (1992) - [c3]Felipe Cucker, Francesc Rosselló:
On the Complexity of Some Problems for the Blum, Shub & Smale Model. LATIN 1992: 117-129 - 1991
- [c2]Felipe Cucker, A. Torrecillas:
Two P-Complete Problems in the Theory of the Reals. ICALP 1991: 556-565 - 1990
- [j3]Felipe Cucker, Marie-Françoise Roy:
A Theorem on Random Polynomials and Some Consequences in Average Complexity. J. Symb. Comput. 10(5): 405-410 (1990)
1980 – 1989
- 1989
- [j2]Felipe Cucker, Joaquim Gabarró:
Non Recursive Functions Have Transcendental Generating Series. RAIRO Theor. Informatics Appl. 23(4): 445-448 (1989) - [j1]Jorge Castro, Felipe Cucker:
Nondeterministic Ω-Computations and the Analytical Hierarchy. Math. Log. Q. 35(4): 333-342 (1989) - 1987
- [c1]Felipe Cucker, Luis Miguel Pardo, Mario Raimondo, Tomás Recio, Marie-Françoise Roy:
On the Computation of the Local and Global Analytic Branches of a Real Algebraic Curve. AAECC 1987: 161-181
Coauthor Index
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