04682nam 2200589 450 991048085880332120170821170443.01-4704-1409-0(CKB)3780000000000293(EBL)3113185(SSID)ssj0001255897(PQKBManifestationID)11714728(PQKBTitleCode)TC0001255897(PQKBWorkID)11258899(PQKB)10677080(MiAaPQ)EBC3113185(PPN)197102484(EXLCZ)99378000000000029320140612h20132013 uy 0engur|n|---|||||txtccrRecent advances in real complexity and computation UIMP-RSME Lluis Santaló Summer School 2012, recent advances in real complexity and computation, July 16-20, 2012, UIMP Palacio de la Magdlena, Santander (Cantabria), Spain /Jose Luis Montaña, Luis M. Pardo, editorsProvidence, Rhode Island :American Mathematical Society,2013.©20131 online resource (202 p.)Contemporary Mathematics,1098-3627 ;Volume 604Description based upon print version of record.0-8218-9150-2 Includes bibliographical references.""Editorsâ€? preface""; ""Topics in real and complex number complexity theory""; ""1. Introduction""; ""2. A motivating example""; ""3. The real number model by Blum, Shub, and Smale""; ""4. Structural complexity""; ""5. Probabilistically checkable proofs over â??""; ""Acknowledgement""; ""References""; ""Polar, bipolar and copolar varieties: Real solving of algebraic varieties with intrinsic complexity""; ""1. Introduction""; ""2. Notations and statement of results""; ""3. Polar varieties""; ""4. The smooth case""; ""5. Tools to handle the singular case""""6. Bipolar varieties and real point finding in the singular case""""References""; ""The complexity and geometry of numerically solving polynomial systems.""; ""1. The modern numerical approach to polynomial system solving""; ""2. A technical description of the problem""; ""3. Geometry and condition number""; ""4. The complexity of following a homotopy path""; ""5. The problem of good starting points""; ""6. The condition Lipschitzâ€?Riemannian structure""; ""7. Condition geodesics and the geometry of \CW""; ""8. The univariate case and elliptic Fekete points""""9. The algebraic eigenvalue problem""""Appendix A. A model of computation for machines with round-off and input errors""; ""References""; ""Multiplicity hunting and approximating multiple roots of polynomial systems""; ""1. Introduction""; ""2. Multiplicity. Algebraic geometric point of view""; ""3. Multiplicity. Numerical point of view""; ""4. Multiplicity and homotopy methods""; ""5. Recovering the quadratic convergence""; ""6. Deflating and kerneling""; ""7. Examples""; ""8. Conclusion and future work""; ""References""""On the intrinsic complexity of elimination problems in effective algebraic geometry""""1. Introduction""; ""2. Concepts and tools from algebraic geometry""; ""3. Robust parameterized arithmetic circuits""; ""4. A family of hard elimination polynomials""; ""5. A computation model with robust parameterized arithmetic circuits""; ""6. Applications to elimination theory""; ""References""; ""Newton iteration, conditioning and zero counting""; ""1. Introduction""; ""Part 1. Newton Iteration and Alpha theory""; ""2. Outline""; ""3. The gamma invariant""; ""4. The -Theorems""""5. Estimates from data at a point""""Part 2. Inclusion and exclusion""; ""6. Eckart-Young theorem""; ""7. The space of homogeneous polynomial systems""; ""8. The condition number""; ""9. The inclusion theorem""; ""10. The exclusion lemma""; ""Part 3. The algorithm and its complexity""; ""11. Convexity and geometry Lemmas""; ""12. The counting algorithm""; ""13. Complexity""; ""14. Probabilistic and smoothed analysis""; ""15. Conclusions""; ""References""Contemporary mathematics (American Mathematical Society) ;Volume 604.Computational complexityCongressesElectronic books.Computational complexity511.3/52Montana Jose Luis1961-Pardo L. M(Luis M.),UIMP-RSME Lluis Santalâo SummerMiAaPQMiAaPQMiAaPQBOOK9910480858803321Recent advances in real complexity and computation2295057UNINA