# Tractability of Multivariate Problems: Volume III: Standard Information for Operators

Share this page
*Erich Novak; Henryk Woźniakowski*

A publication of the European Mathematical Society

This is the third volume of a three-volume 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 high-dimensional
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.

#### Readership

Graduate students and research mathematicians interested in computational mathematics.