Michael Shub

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Computational Complexity: On the Geometry of Polynomials and a Theory of Cost: II

Stephen Smale, Michael Shub, S. Smale, 1986, SIAM J. Comput..

Complexity of Bezout’s Theorem VII: Distance Estimates in the Condition Metric

Michael Shub, Carlos Beltrán, M. Shub, 2009, Found. Comput. Math..

Convexity Properties of the Condition Number II

Michael Shub, Carlos Beltrán, Gregorio Malajovich, 2009, SIAM J. Matrix Anal. Appl..

Multihomogeneous Newton methods

Michael Shub, Jean-Pierre Dedieu, 2000, Math. Comput..

A Simple Unpredictable Pseudo-Random Number Generator

Manuel Blum, Michael Shub, Lenore Blum, 1986, SIAM J. Comput..

Unified complexity analysis for Newton LP methods

James Renegar, Michael Shub, M. Shub, 1992, Math. Program..

COMPLEXITY AND REAL COMPUTATION: A MANIFESTO

Felipe Cucker, Steve Smale, Michael Shub, 1996 .

Complexity of Bezout's Theorem: III. Condition Number and Packing

Stephen Smale, Michael Shub, S. Smale, 1993, J. Complex..

Adaptative Step Size Selection for Homotopy Methods to Solve Polynomial Equations pdf

Michael Shub, Gregorio Malajovich, Jean-Pierre Dedieu, 2011, ArXiv.

A Note on the Finite Variance of the Averaging Function for Polynomial System Solving

Michael Shub, Carlos Beltrán, 2010, Found. Comput. Math..

Smale horseshoe

Stephen Smale, Michael Shub, S. Smale, 2007, Scholarpedia.

Newton Flow and interior Point Methods in Linear Programming

Michael Shub, Jean-Pierre Dedieu, M. Shub, 2005, Int. J. Bifurc. Chaos.

On the asymptotic behavior of the projective rescaling algorithm for linear programming

Michael Shub, M. Shub, 1987, J. Complex..

The complexity and geometry of numerically solving polynomial systems

Michael Shub, Carlos Beltran, M. Shub, 2012, 1211.1528.

Test complexity of generic polynomials

Thomas Lickteig, Michael Shub, Peter Bürgisser, 1992, J. Complex..

Selected papers of a conference on Foundations of computational mathematics

Felipe Cucker, Michael Shub, 1997 .

Erratum to: Smale’s Fundamental Theorem of Algebra Reconsidered

Michael Shub, Diego Armentano, M. Shub, 2014, Foundations of Computational Mathematics.

From Topology to Computation: Proceedings of the Smalefest

Jerrold E. Marsden, Stephen Smale, Michael Shub, 2011 .

Smale’s Fundamental Theorem of Algebra Reconsidered

Michael Shub, Diego Armentano, M. Shub, 2012, Found. Comput. Math..

Convexity Properties of the Condition Number

Michael Shub, Carlos Beltrán, Gregorio Malajovich, 2008, SIAM J. Matrix Anal. Appl..

Implicit Gamma Theorems (I): Pseudoroots and Pseudospectra

Myong-Hi Kim, Michael Shub, Jean-Pierre Dedieu, 2003, Found. Comput. Math..

On the Curvature of the Central Path of Linear Programming Theory

Michael Shub, Gregorio Malajovich, Jean-Pierre Dedieu, 2003, Found. Comput. Math..

Foundations of Computational Mathematics

Felipe Cucker, Michael Shub, 1997 .

On simple double zeros and badly conditioned zeros of analytic functions of n variables

Michael Shub, Jean-Pierre Dedieu, M. Shub, 2001, Math. Comput..

Computing the Homology of Real Projective Sets

Felipe Cucker, Michael Shub, Teresa Krick, 2016, Foundations of Computational Mathematics.

Stably Ergodic Dynamical Systems and Partial Hyperbolicity

Michael Shub, Charles Pugh, M. Shub, 1997, J. Complex..

Newton's method for overdetermined systems of equations

Michael Shub, Jean-Pierre Dedieu, M. Shub, 2000, Math. Comput..

Morse-Smale systems

Michael Shub, 2007, Scholarpedia.

Preface

Michael Shub, Brenda L. Dietrich, 2003, IBM J. Res. Dev..

Complexity of Bezout's Theorem V: Polynomial Time

Stephen Smale, Michael Shub, S. Smale, 1994, Theor. Comput. Sci..

The implicit function theorem revisited

Michael Shub, 1994, IBM J. Res. Dev..

1998 Best Paper Award

Michael Shub, Joseph F. Traub, Peter Kirrinnis, 1998, J. Complex..

On the Geometry and Topology of the Solution Variety for Polynomial System Solving

Michael Shub, Carlos Beltrán, M. Shub, 2012, Found. Comput. Math..

Boundary Behavior of Interior Point Algorithms in Linear Programming

Nimrod Megiddo, Michael Shub, N. Megiddo, 1989, Math. Oper. Res..

Complexity of Bezout’s Theorem VI: Geodesics in the Condition (Number) Metric

Michael Shub, M. Shub, 2007, Found. Comput. Math..

On a theory of computation over the real numbers; NP completeness, recursive functions and universal machines

Stephen Smale, Michael Shub, Lenore Blum, 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

Condition Length and Complexity for the Solution of Polynomial Systems

Felipe Cucker, Michael Shub, Peter Bürgisser, 2015, Found. Comput. Math..

Evaluating Rational Functions: Infinite Precision is Finite Cost and Tractable on Average (Extended Abstract)

Michael Shub, Lenore Blum, 1984, FOCS.

Guest Editor's Introduction

Michael Shub, 1997, J. Complex..

Separation of Complexity Classes in Koiran's Weak Model

Felipe Cucker, Stephen Smale, Michael Shub, 1994, Theor. Comput. Sci..

On the existence of generally convergent algorithms

Stephen Smale, Michael Shub, S. Smale, 1986, J. Complex..

FROM DYNAMICS TO COMPUTATION AND BACK

Michael Shub, M. Shub, 2002 .

Generalized Knapsack Problems and Fixed Degree Separations

Felipe Cucker, Michael Shub, M. Shub, 1996, Theor. Comput. Sci..

Evaluating Rational Functions: Infinite Precision is Finite Cost and Tractable on Average

Michael Shub, Lenore Blum, M. Shub, 1984, SIAM J. Comput..

On the distance to the zero set of a homogeneous polynomial

Michael Shub, 1989, J. Complex..

Future stability is not generic

Michael Shub, R. F. Williams, M. Shub, 1969 .

Editor's Foreword

Felipe Cucker, Michael Shub, 1996, J. Complex..

Editorial

Michael Shub, 2001, Found. Comput. Math..

A Theory of NP-completeness and Ill-conditioning for Approximate Real Computations

Michael Shub, Gregorio Malajovich, M. Shub, 2018, J. ACM.

Foreword

James Renegar, Felipe Cucker, Tomaso A. Poggio, 2005, Found. Comput. Math..

Comparison of Two Pseudo-Random Number Generators

Manuel Blum, Michael Shub, Lenore Blum, 1982, CRYPTO.

Real Computation and Complexity (Dagstuhl Seminar 04061)

Thomas Lickteig, Felipe Cucker, Michael Shub, 2021 .

Disease Prediction with a Maximum Entropy Method pdf

Michael Shub, Qing Xu, Xiaohua Xuan, 2021, ArXiv.

Ergodic elements of ergodic actions

Michael Shub, M. Shub, C. Pugh, 1971 .

Some Remarks on Bezout’s Theorem and Complexity Theory

Michael Shub, M. Shub, 1993 .

Ergodicity of Anosov actions

Michael Shub, M. Shub, C. Pugh, 1972 .

Newton’s Method

Felipe Cucker, Michael Shub, Lenore Blum, 1998 .

On the average cost of solving polynomial equations

Michael Shub, Steve Smale, 1983 .

DIFFERENTIABILITY AND CONTINUITY OF INVARIANT MANIFOLDS *

Michael Shub, M. Shub, C. Pugh, 1980 .

FILTRATIONS, DECOMPOSITIONS, AND EXPLOSIONS.

Michael Shub, Zbigniew Nitecki, M. Shub, 1975 .

Algebraic Settings for the Problem “P ≠ NP?”

Felipe Cucker, Michael Shub, Lenore Blum, 1998 .

Neighborhoods of hyperbolic sets

Michael Shub, Morris W. Hirsch, Jacob Palis, 1970 .

The local theory of normally hyperbolic, invariant, compact manifolds

Michael Shub, Morris W. Hirsch, M. Hirsch, 1977 .

On simple zeros of analytic functions of n variables

Michael Shub, Jean-Pierre Dedieu, 2001 .

Information, Uncertainty, Complexity (J. F. Traub, G. W. Wasilkowski and H. Woźniakowski)

Michael Shub, 1987 .

Endomorphisms of compact differentiable manifolds

Michael Shub, M. Shub, 1969 .

Stably ergodic diffeomorphisms

Michael Shub, M. Shub, C. Pugh, 1994 .

The Newtonian graph of a complex polynomial

Michael Shub, David Tischler, R. F. Williams, 1988 .

Corrigendum to: Stable ergodicity and julienne quasi-conformality, J. Eur. Math. Soc. 2, 1-52

Michael Shub, Charles C. Pugh, Alexander Starkov, 2004 .

The integral homology of smale diffeomorphisms

Michael Shub, M. Maller, 1985 .