LEADER 02907nam 22003975a 450 001 9910153614503321 005 20121029234500.0 010 $a3-03719-616-5 024 70$a10.4171/116 035 $a(CKB)3710000000962496 035 $a(CH-001817-3)159-121029 035 $a(PPN)178156159 035 $a(EXLCZ)993710000000962496 100 $a20121029j20121029 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTractability of Multivariate Problems$b[electronic resource] $eVolume III: Standard Information for Operators /$fErich Novak, Henryk Woz?niakowski 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2012 215 $a1 online resource (604 pages) 225 0 $aEMS Tracts in Mathematics (ETM)$v18 330 $aThis three-volume set is a comprehensive study of the tractability of multivariate problems. Volume I covers algorithms using linear information consisting of arbitrary continuous linear functionals. Volumes II and III are devoted to algorithms using standard information consisting of function values. Approximation of linear and selected nonlinear functionals is dealt with in volume II, and linear and selected nonlinear operators are studied in volume III. To a large extent, volume III can be read independently of volumes I and II. The most important example studied in volume III is the approximation of multivariate functions. It turns out that many other linear and some nonlinear problems are closely related to the approximation of multivariate functions. While the lower bounds obtained in volume I for the class of linear information also yield lower bounds for the standard class of function values, new techniques for upper bounds are presented in volume III. One of the main issues here is to verify when the power of standard information is nearly the same as the power of linear information. In particular, for the approximation problem defined over Hilbert spaces, the power of standard and linear information is the same in the randomized and average case (with Gaussian measures) settings, whereas in the worst case setting this is not true. The book is of interest to researchers working in computational mathematics, especially in approximation of high-dimensiona problems. It may be well suited for graduate courses and seminars. The text contains 58 open problems for future research in tractability. 606 $aNumerical analysis$2bicssc 606 $aNumerical analysis$2msc 615 07$aNumerical analysis 615 07$aNumerical analysis 686 $a65-xx$2msc 700 $aNovak$b Erich$056070 702 $aWoz?niakowski$b Henryk 801 0$bch0018173 906 $aBOOK 912 $a9910153614503321 996 $aTractability of Multivariate Problems$92565018 997 $aUNINA