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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
| 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 |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2013 |
| Descrizione fisica | 1 online resource (202 p.) |
| Disciplina | 511.3/52 |
| Collana | Contemporary Mathematics |
| Soggetto topico | Computational complexity |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-1409-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 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 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"" |
| Record Nr. | UNINA-9910480858803321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
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
| 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 |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2013 |
| Descrizione fisica | 1 online resource (202 p.) |
| Disciplina | 511.3/52 |
| Collana | Contemporary mathematics |
| Soggetto topico | Computational complexity |
| ISBN | 1-4704-1409-0 |
| Classificazione | 03D1514Qxx14Q2049Q1565-XX65H20 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Editors' 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 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. |
| Record Nr. | UNINA-9910796032303321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
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
| 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 |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2013 |
| Descrizione fisica | 1 online resource (202 p.) |
| Disciplina | 511.3/52 |
| Collana | Contemporary mathematics |
| Soggetto topico | Computational complexity |
| ISBN | 1-4704-1409-0 |
| Classificazione | 03D1514Qxx14Q2049Q1565-XX65H20 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Editors' 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 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. |
| Record Nr. | UNINA-9910811619803321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||