Hardcover ISBN:  9783037191163 
Product Code:  EMSTM/18 
List Price:  $128.00 
AMS Member Price:  $102.40 
Hardcover ISBN:  9783037191163 
Product Code:  EMSTM/18 
List Price:  $128.00 
AMS Member Price:  $102.40 

Book DetailsEMS Tracts in MathematicsVolume: 18; 2012; 604 ppMSC: Primary 65; 68; 41; 46; 28
This is the third volume of a threevolume set comprising a comprehensive study of the tractability of multivariate problems. The third volume deals with algorithms using standard information consisting of function values. Linear and selected nonlinear operators are studied.
The most important example studied in volume III is the approximation of multivariate functions. 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 highdimensional problems. It may be well suited for graduate courses and seminars. The text contains 58 open problems for future research in tractability.
A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
ReadershipGraduate students and research mathematicians interested in computational mathematics.

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This is the third volume of a threevolume set comprising a comprehensive study of the tractability of multivariate problems. The third volume deals with algorithms using standard information consisting of function values. Linear and selected nonlinear operators are studied.
The most important example studied in volume III is the approximation of multivariate functions. 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 highdimensional problems. It may be well suited for graduate courses and seminars. The text contains 58 open problems for future research in tractability.
A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
Graduate students and research mathematicians interested in computational mathematics.