A Numerical Algorithm for Zero Counting. I: Complexity and Accuracy

[1]  Nicholas J. Higham,et al.  INVERSE PROBLEMS NEWSLETTER , 1991 .

[2]  S. Smale,et al.  Complexity of Bézout’s theorem. I. Geometric aspects , 1993 .

[3]  George E. Collins,et al.  Quantifier elimination for real closed fields by cylindrical algebraic decomposition , 1975 .

[4]  Nicolai Vorobjov,et al.  Counting connected components of a semialgebraic set in subexponential time , 1992, computational complexity.

[5]  Joos Heintz,et al.  Single Exponential Path Finding in Semialgebraic Sets. Part 1: The Case of a Regular Bounded Hypersurface , 1990, AAECC.

[6]  Marc Giusti,et al.  Generalized polar varieties: geometry and algorithms , 2005, J. Complex..

[7]  Joos Heintz,et al.  Single Exponential Path Finding in Semi-algebraic Sets, Part II: The General Case , 1994 .

[8]  Richard E. Ewing,et al.  "The Merging of Disciplines: New Directions in Pure, Applied, and Computational Mathematics" , 1986 .

[9]  Dima Grigoriev,et al.  Solving Systems of Polynomial Inequalities in Subexponential Time , 1988, J. Symb. Comput..

[10]  Felipe Cucker,et al.  Complexity estimates depending on condition and round-off error , 1998, JACM.

[11]  Ding-Xuan Zhou,et al.  Learning Theory: An Approximation Theory Viewpoint , 2007 .

[12]  H. R. Wüthrich,et al.  Ein Entscheidungsverfahren für die Theorie der reell- abgeschlossenen Körper , 1976, Komplexität von Entscheidungsproblemen 1976.

[13]  S. Smale,et al.  Complexity of Bezout's theorem IV: probability of success; extensions , 1996 .

[14]  A. Tarski.  A Decision Method for Elementary Algebra and Geometry , 2023 .

[15]  Yijie Han,et al.  An efficient and fast parallel-connected component algorithm , 1990, JACM.

[16]  Felipe Cucker,et al.  A Primal-Dual Algorithm for Solving Polyhedral Conic Systems with a Finite-Precision Machine , 2002, SIAM J. Optim..

[17]  Felipe Cucker,et al.  Solving linear programs with finite precision: II. Algorithms , 2006, J. Complex..

[18]  P. Priouret,et al.  Newton's method on Riemannian manifolds: covariant alpha theory , 2002, math/0209096.

[19]  Gregorio Malajovich,et al.  On Generalized Newton Algorithms: Quadratic Convergence, Path-Following and Error Analysis , 1994, Theor. Comput. Sci..

[20]  Felipe Cucker,et al.  Approximate Zeros and Condition Numbers , 1999, J. Complex..

[21]  C. Bajaj.  Algebraic Geometry and its Applications , 1994 .

[22]  W. Böge,et al.  Quantifier Elimination for Real Closed Fields , 1985, AAECC.

[23]  S. Smale.  Newton’s Method Estimates from Data at One Point , 1986 .

[24]  Klaus Meer.  Counting problems over the reals , 2000, Theor. Comput. Sci..

[25]  Felipe Cucker,et al.  Counting complexity classes for numeric computations II: algebraic and semialgebraic sets , 2003, STOC '04.

[26]  E. Condon.  The Theory of Groups and Quantum Mechanics , 1932 .

[27]  Felipe Cucker,et al.  Learning Theory: An Approximation Theory Viewpoint (Cambridge Monographs on Applied & Computational Mathematics) , 2007 .

[28]  Lenore Blum,et al.  Complexity and Real Computation , 1997, Springer New York.

[29]  Stephen Smale,et al.  Complexity of Bezout's Theorem: III. Condition Number and Packing , 1993, J. Complex..

[30]  Dima Grigoriev,et al.  Complexity of Deciding Tarski Algebra , 1988, J. Symb. Comput..

[31]  D. Grigor'ev.  Complexity of deciding Tarski algebra , 1988 .

[32]  Tien-Yien Li.  Numerical Solution of Polynomial Systems by Homotopy Continuation Methods , 2003 .