Recent 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, editors

• Pubblicazione: Providence, Rhode Island : , : American Mathematical Society, , 2013; ©2013
• Descrizione fisica: 1 online resource (202 p.)
• Disciplina: 511.3/52
• Soggetto topico: Computational complexity
• Soggetto genere / forma: Electronic books.
• Persona (resp. second.): MontanaJose Luis <1961->; PardoL. M (Luis M.)
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""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""
• Titolo autorizzato: Recent advances in real complexity and computation
• ISBN: 1-4704-1409-0
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910480858803321
• Lo trovi qui: Univ. Federico II
• Serie: Contemporary mathematics (American Mathematical Society) ; ; Volume 604.