LEADER 04682nam 2200589 450 001 9910480858803321 005 20170821170443.0 010 $a1-4704-1409-0 035 $a(CKB)3780000000000293 035 $a(EBL)3113185 035 $a(SSID)ssj0001255897 035 $a(PQKBManifestationID)11714728 035 $a(PQKBTitleCode)TC0001255897 035 $a(PQKBWorkID)11258899 035 $a(PQKB)10677080 035 $a(MiAaPQ)EBC3113185 035 $a(PPN)197102484 035 $a(EXLCZ)993780000000000293 100 $a20140612h20132013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aRecent advances in real complexity and computation $eUIMP-RSME Lluis Santalo? Summer School 2012, recent advances in real complexity and computation, July 16-20, 2012, UIMP Palacio de la Magdlena, Santander (Cantabria), Spain /$fJose Luis Montan?a, Luis M. Pardo, editors 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2013. 210 4$d©2013 215 $a1 online resource (202 p.) 225 1 $aContemporary Mathematics,$x1098-3627 ;$vVolume 604 300 $aDescription based upon print version of record. 311 $a0-8218-9150-2 320 $aIncludes bibliographical references. 327 $a""Editorsa??? 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 a???""; ""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"" 327 $a""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 Lipschitza???Riemannian structure""; ""7. Condition geodesics and the geometry of \CW""; ""8. The univariate case and elliptic Fekete points"" 327 $a""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"" 327 $a""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"" 327 $a""5. Estimates from data at a point""""Part 2. Inclusion and exclusion""; ""6. Eckart-Young theorem""; ""7. The space of homogeneous polynomial systems""; ""8. The condition number""; ""9. The inclusion theorem""; ""10. The exclusion lemma""; ""Part 3. The algorithm and its complexity""; ""11. Convexity and geometry Lemmas""; ""12. The counting algorithm""; ""13. Complexity""; ""14. Probabilistic and smoothed analysis""; ""15. Conclusions""; ""References"" 410 0$aContemporary mathematics (American Mathematical Society) ;$vVolume 604. 606 $aComputational complexity$vCongresses 608 $aElectronic books. 615 0$aComputational complexity 676 $a511.3/52 702 $aMontana$b Jose Luis$f1961- 702 $aPardo$b L. M$g(Luis M.), 712 12$aUIMP-RSME Lluis Santalâo Summer 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480858803321 996 $aRecent advances in real complexity and computation$92295057 997 $aUNINA