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Record Nr. |
UNINA9910480858803321 |
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Titolo |
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 |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , 2013 |
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©2013 |
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ISBN |
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Descrizione fisica |
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1 online resource (202 p.) |
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Collana |
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Contemporary Mathematics, , 1098-3627 ; ; Volume 604 |
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Disciplina |
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Soggetti |
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Computational complexity |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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""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 Lipschitz�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 |
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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"" |
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