Felipe Cucker

Anders C. Hansen

CoRR, 2023

2022

On the Complexity of the Plantinga-Vegter Algorithm.

[BibT_eX]

[DOI]

Alperen Ali Ergür

Discret. Comput. Geom., 2022

2021

Computing the Homology of Semialgebraic Sets. II: General Formulas.

[BibT_eX]

[DOI]

Found. Comput. Math., 2021

Functional norms, condition numbers and numerical algorithms in algebraic geometry.

[BibT_eX]

[DOI]

Alperen Ali Ergür

CoRR, 2021

2020

On local analysis.

[BibT_eX]

[DOI]

Teresa Krick

J. Complex., 2020

Computing the Homology of Semialgebraic Sets. I: Lax Formulas.

[BibT_eX]

[DOI]

Found. Comput. Math., 2020

Rigid continuation paths II. Structured polynomial systems.

[BibT_eX]

[DOI]

Pierre Lairez

CoRR, 2020

2019

On Flocks Under Switching Directed Interaction Topologies.

[BibT_eX]

[DOI]

Jiu-Gang Dong

SIAM J. Appl. Math., 2019

Computing the Homology of Basic Semialgebraic Sets in Weak Exponential Time.

[BibT_eX]

[DOI]

Pierre Lairez

J. ACM, 2019

Plantinga-Vegter Algorithm takes Average Polynomial Time.

[BibT_eX]

[DOI]

Alperen Ali Ergür

Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation, 2019

Recent Advances in the Computation of the Homology of Semialgebraic Sets.

[BibT_eX]

[DOI]

Proceedings of the Computing with Foresight and Industry, 2019

2018

Computing the Homology of Real Projective Sets.

[BibT_eX]

[DOI]

Teresa Krick

Michael Shub

Found. Comput. Math., 2018

2017

On the condition of the zeros of characteristic polynomials.

[BibT_eX]

[DOI]

Elisa Rocha Cardozo

J. Complex., 2017

2016

Condition Length and Complexity for the Solution of Polynomial Systems.

[BibT_eX]

[DOI]

Found. Comput. Math., 2016

Probabilistic analyses of condition numbers.

[BibT_eX]

[DOI]

Acta Numer., 2016

2015

Solving second-order conic systems with variable precision.

[BibT_eX]

[DOI]

Vera Roshchina

Math. Program., 2015

A Randomized Homotopy for the Hermitian Eigenpair Problem.

[BibT_eX]

[DOI]

Diego Armentano

Found. Comput. Math., 2015

Complexity of Symbolic and Numerical Problems (Dagstuhl Seminar 15242).

[BibT_eX]

[DOI]

Marek Karpinski

Nicolai N. Vorobjov Jr.

Dagstuhl Reports, 2015

2014

Fast computation of zeros of polynomial systems with bounded degree under finite-precision.

[BibT_eX]

[DOI]

Math. Comput., 2014

A Theory of Complexity, Condition and Roundoff.

[BibT_eX]

[DOI]

CoRR, 2014

2013

On the Average Condition of Random Linear Programs.

[BibT_eX]

[DOI]

SIAM J. Optim., 2013

Condition - The Geometry of Numerical Algorithms.

[BibT_eX]

[DOI]

Grundlehren der mathematischen Wissenschaften 349, Springer, ISBN: 978-3-642-38895-8, 2013

2012

A numerical algorithm for zero counting. III: Randomization and condition.

[BibT_eX]

[DOI]

Adv. Appl. Math., 2012

The Legacy of Turing in Numerical Analysis.

[BibT_eX]

[DOI]

Proceedings of the SOFSEM 2012: Theory and Practice of Computer Science, 2012

2011

A General Collision-Avoiding Flocking Framework.

[BibT_eX]

[DOI]

Jiu-Gang Dong

IEEE Trans. Autom. Control., 2011

2010

Avoiding Collisions in Flocks.

[BibT_eX]

[DOI]

Jiu-Gang Dong

IEEE Trans. Autom. Control., 2010

Smoothed Analysis of Moore-Penrose Inversion.

[BibT_eX]

[DOI]

SIAM J. Matrix Anal. Appl., 2010

Adversarial smoothed analysis.

[BibT_eX]

[DOI]

Raphael A. Hauser

Martin Lotz

J. Complex., 2010

On strata of degenerate polyhedral cones, II: Relations between condition measures.

[BibT_eX]

[DOI]

J. Complex., 2010

Solving polynomial equations in smoothed polynomial time and a near solution to smale's 17th problem.

[BibT_eX]

[DOI]

Proceedings of the 42nd ACM Symposium on Theory of Computing, 2010

2009

Componentwise Condition Numbers of Random Sparse Matrices.

[BibT_eX]

[DOI]

SIAM J. Matrix Anal. Appl., 2009

Exotic Quantifiers, Complexity Classes, and Complete Problems.

[BibT_eX]

[DOI]

Found. Comput. Math., 2009

On strata of degenerate polyhedral cones I: Condition and distance to strata.

[BibT_eX]

[DOI]

Eur. J. Oper. Res., 2009

A Numerical Algorithm for Zero Counting. II: Distance to Ill-posedness and Smoothed Analysis

[BibT_eX]

[DOI]

CoRR, 2009

Parallel Time and Quantifier Prefixes.

[BibT_eX]

[DOI]

Comput. Complex., 2009

2008

A Condition Number for Multifold Conic Systems.

[BibT_eX]

[DOI]

SIAM J. Optim., 2008

The probability that a slightly perturbed numerical analysis problem is difficult.

[BibT_eX]

[DOI]

Martin Lotz

Math. Comput., 2008

A numerical algorithm for zero counting, I: Complexity and accuracy.

[BibT_eX]

[DOI]

J. Complex., 2008

2007

Emergent Behavior in Flocks.

[BibT_eX]

[DOI]

IEEE Trans. Autom. Control., 2007

On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems.

[BibT_eX]

[DOI]

Huaian Diao

Yimin Wei

Math. Comput., 2007

A note on parallel and alternating time.

[BibT_eX]

[DOI]

Irénée Briquel

J. Complex., 2007

2006

Smoothed analysis of some condition numbers.

[BibT_eX]

[DOI]

Huaian Diao

Yimin Wei

Numer. Linear Algebra Appl., 2006

Solving linear programs with finite precision: II. Algorithms.

[BibT_eX]

[DOI]

J. Complex., 2006

Counting complexity classes for numeric computations II: Algebraic and semialgebraic sets.

[BibT_eX]

[DOI]

J. Complex., 2006

Implicit complexity over an arbitrary structure: Quantifier alternations.

[BibT_eX]

[DOI]

Inf. Comput., 2006

The complexity of semilinear problems in succinct representation.

[BibT_eX]

[DOI]

Comput. Complex., 2006

2005

Tail Decay and Moment Estimates of a Condition Number for Random Linear Conic Systems.

[BibT_eX]

[DOI]

Raphael A. Hauser

SIAM J. Optim., 2005

Implicit Complexity over an Arbitrary Structure: Sequential and Parallel Polynomial Time.

[BibT_eX]

[DOI]

J. Log. Comput., 2005

A note on level-2 condition numbers.

[BibT_eX]

[DOI]

J. Complex., 2005

Counting Complexity Classes for Numeric Computations. III: Complex Projective Sets.

[BibT_eX]

[DOI]

Martin Lotz

Found. Comput. Math., 2005

Foreword.

[BibT_eX]

[DOI]

Found. Comput. Math., 2005

On sparseness, reducibilities, and complexity.

[BibT_eX]

[DOI]

Ann. Pure Appl. Log., 2005

2004

Solving linear programs with finite precision: I. Condition numbers and random programs.

[BibT_eX]

[DOI]

Math. Program., 2004

Modeling Language Evolution.

[BibT_eX]

[DOI]

Ding-Xuan Zhou

Found. Comput. Math., 2004

Tailoring Recursion to Characterize Non-Deterministic Complexity Classes over Arbitrary Structures.

[BibT_eX]

[DOI]

Proceedings of the Exploring New Frontiers of Theoretical Informatics, 2004

2003

Counting Complexity Classes for Numeric Computations I: Semilinear Sets.

[BibT_eX]

[DOI]

SIAM J. Comput., 2003

On the Expected Condition Number of Linear Programming Problems.

[BibT_eX]

[DOI]

Mario Wschebor

Numerische Mathematik, 2003

Unifying Condition Numbers for Linear Programming.

[BibT_eX]

[DOI]

Math. Oper. Res., 2003

Learning from rounded-off data.

[BibT_eX]

[DOI]

Inf. Comput., 2003

Safe Recursion Over an Arbitrary Structure: PAR, PH and DPH.

[BibT_eX]

[DOI]

Proceedings of the Fifth International Workshop on Implicit Computational Complexity, 2003

Counting Complexity Classes over the Reals I: The Additive Case.

[BibT_eX]

[DOI]

Proceedings of the Algorithms and Computation, 14th International Symposium, 2003

Computability over an Arbitrary Structure. Sequential and Parallel Polynomial Time.

[BibT_eX]

[DOI]

Proceedings of the Foundations of Software Science and Computational Structures, 2003

2002

A Primal-Dual Algorithm for Solving Polyhedral Conic Systems with a Finite-Precision Machine.

[BibT_eX]

[DOI]

SIAM J. Optim., 2002

Real Computations with Fake Numbers.

[BibT_eX]

[DOI]

J. Complex., 2002

Best Choices for Regularization Parameters in Learning Theory: On the Bias-Variance Problem.

[BibT_eX]

[DOI]

Found. Comput. Math., 2002

On sparseness and Turing reducibility over the reals.

[BibT_eX]

[DOI]

Proceedings of the 9th Workhop on Logic, Language, Information and Computation, 2002

2001

On weak and weighted computations over the real closure of Q.

[BibT_eX]

[DOI]

Theor. Comput. Sci., 2001

There are No Sparse NPw-Hard Sets.

[BibT_eX]

[DOI]

Dima Grigoriev

SIAM J. Comput., 2001

A new condition number for linear programming.

[BibT_eX]

[DOI]

Math. Program., 2001

2000

Preface.

[BibT_eX]

[DOI]

Thomas Lickteig

J. Complex., 2000

Solving polynomial systems: a complexity theory viewpoint.

[BibT_eX]

[DOI]

Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation, 2000

1999

Logics Which Capture Complexity Classes Over The Reals.

[BibT_eX]

[DOI]

Klaus Meer

J. Symb. Log., 1999

A Polynomial Time Algorithm for Diophantine Equations in One Variable.

[BibT_eX]

[DOI]

Pascal Koiran

J. Symb. Comput., 1999

Complexity Lower Bounds for Approximation Algebraic Computation Trees.

[BibT_eX]

[DOI]

Dima Grigoriev

J. Complex., 1999

Approximate Zeros and Condition Numbers.

[BibT_eX]

[DOI]

J. Complex., 1999

Complexity Estimates Depending on Condition and Round-Off Error.

[BibT_eX]

[DOI]

J. ACM, 1999

1997

On the Power of Real Turing Machines Over Binary Inputs.

[BibT_eX]

[DOI]

Dima Grigoriev

SIAM J. Comput., 1997

Machines Over the Reals and Non Uniformity.

[BibT_eX]

[DOI]

Math. Log. Q., 1997

Complexity and Dimension.

[BibT_eX]

[DOI]

Pascal Koiran

Martín Matamala

Inf. Process. Lett., 1997

1996

Generalized Knapsack Problems and Fixed Degree Separations.

[BibT_eX]

[DOI]

Mike Shub

Theor. Comput. Sci., 1996

On Digital Nondeterminism.

[BibT_eX]

[DOI]

Martín Matamala

Math. Syst. Theory, 1996

EDITOR'S FOREWORD.

[BibT_eX]

[DOI]

Michael Shub

J. Complex., 1996

1995

Computing over the Reals with Addition and Order: Higher Complexity Classes.

[BibT_eX]

[DOI]

Pascal Koiran

J. Complex., 1995

On real Turing machines that toss coins.

[BibT_eX]

[DOI]

Proceedings of the Twenty-Seventh Annual ACM Symposium on Theory of Computing, 1995

1994

Separation of Complexity Classes in Koiran's Weak Model.

[BibT_eX]

[DOI]

Mike Shub

Theor. Comput. Sci., 1994

1993

On the Complexity of Quantifier Elimination: the Structural Approach.

[BibT_eX]

[DOI]

Comput. J., 1993

Recursiveness over the Complex Numbers is Time-Bounded.

[BibT_eX]

[DOI]

Francesc Rosselló

Proceedings of the Foundations of Software Technology and Theoretical Computer Science, 1993

1992

The Arithmetical Hierarchy over the Reals.

[BibT_eX]

[DOI]

J. Log. Comput., 1992

Two P-complete problems in the theory of the reals.

[BibT_eX]

[DOI]

A. Torrecillas

J. Complex., 1992

PR != NCR.

[BibT_eX]

[DOI]

J. Complex., 1992

Time Bounded Computations over the Reals.

[BibT_eX]

[DOI]

José L. Montaña

Luis M. Pardo

Int. J. Algebra Comput., 1992

NC Algorithms for Real Algebraic Numbers.

[BibT_eX]

[DOI]

Appl. Algebra Eng. Commun. Comput., 1992

On the Complexity of Some Problems for the Blum, Shub & Smale Model.

[BibT_eX]

[DOI]

Francesc Rosselló

Proceedings of the LATIN '92, 1992

1991

Two P-Complete Problems in the Theory of the Reals.

[BibT_eX]

[DOI]

A. Torrecillas

Proceedings of the Automata, Languages and Programming, 18th International Colloquium, 1991

1990

A Theorem on Random Polynomials and Some Consequences in Average Complexity.

[BibT_eX]

[DOI]

Marie-Françoise Roy

J. Symb. Comput., 1990

1989

Nondeterministic Ω-Computations and the Analytical Hierarchy.

[BibT_eX]

[DOI]

Jorge Castro

Math. Log. Q., 1989

Non Recursive Functions Have Transcendental Generating Series.

[BibT_eX]

[DOI]