LEADER 04613nam 2200553 450 001 9910811619803321 005 20220902012005.0 010 $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(RPAM)17803442 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 ;$v604$x0271-4132 300 $aDescription based upon print version of record. 311 $a0-8218-9150-2 320 $aIncludes bibliographical references. 327 $aEditors' 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 -- 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. 410 0$aContemporary mathematics (American Mathematical Society).$v604$x0271-4132 606 $aComputational complexity$vCongresses 615 0$aComputational complexity 676 $a511.3/52 686 $a03D15$a14Qxx$a14Q20$a49Q15$a65-XX$a65H20$2msc 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 $a9910811619803321 996 $aRecent advances in real complexity and computation$93931866 997 $aUNINA