How Long to Read Tractability of Multivariate Problems: Standard information for functionals

How Long Does it Take to Read Tractability of Multivariate Problems: Standard information for functionals?

It takes the average reader 11 hours and 34 minutes to read Tractability of Multivariate Problems: Standard information for functionals by Erich Novak

Assuming a reading speed of 250 words per minute. Learn more

Description

This is the second volume of a three-volume set comprising a comprehensive study of the tractability of multivariate problems. The second volume deals with algorithms using standard information consisting of function values for the approximation of linear and selected nonlinear functionals. An important example is numerical multivariate integration. The proof techniques used in volumes I and II are quite different. It is especially hard to establish meaningful lower error bounds for the approximation of functionals by using finitely many function values. Here, the concept of decomposable reproducing kernels is helpful, allowing it to find matching lower and upper error bounds for some linear functionals. It is then possible to conclude tractability results from such error bounds. Tractability results, even for linear functionals, are very rich in variety. There are infinite-dimensional Hilbert spaces for which the approximation with an arbitrarily small error of all linear functionals requires only one function value. There are Hilbert spaces for which all nontrivial linear functionals suffer from the curse of dimensionality. This holds for unweighted spaces, where the role of all variables and groups of variables is the same. For weighted spaces one can monitor the role of all variables and groups of variables. Necessary and sufficient conditions on the decay of the weights are given to obtain various notions of tractability. The text contains extensive chapters on discrepancy and integration, decomposable kernels and lower bounds, the Smolyak/sparse grid algorithms, lattice rules and the CBC (component-by-component) algorithms. This is done in various settings. Path integration and quantum computation are also discussed. This volume is of interest to researchers working in computational mathematics, especially in approximation of high-dimensional problems. It is also well suited for graduate courses and seminars. There are 61 open problems listed to stimulate future research in tractability.

How long is Tractability of Multivariate Problems: Standard information for functionals?

Tractability of Multivariate Problems: Standard information for functionals by Erich Novak is 684 pages long, and a total of 173,736 words.

This makes it 231% the length of the average book. It also has 212% more words than the average book.

How Long Does it Take to Read Tractability of Multivariate Problems: Standard information for functionals Aloud?

The average oral reading speed is 183 words per minute. This means it takes 15 hours and 49 minutes to read Tractability of Multivariate Problems: Standard information for functionals aloud.

What Reading Level is Tractability of Multivariate Problems: Standard information for functionals?

Tractability of Multivariate Problems: Standard information for functionals is suitable for students ages 12 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Tractability of Multivariate Problems: Standard information for functionals?

Tractability of Multivariate Problems: Standard information for functionals by Erich Novak is sold by several retailers and bookshops. However, Read Time works with Amazon to provide an easier way to purchase books.

To buy Tractability of Multivariate Problems: Standard information for functionals by Erich Novak on Amazon click the button below.