How Long to Read Tractability of Multivariate Problems: Linear information

How Long Does it Take to Read Tractability of Multivariate Problems: Linear information?

It takes the average reader 6 hours and 45 minutes to read Tractability of Multivariate Problems: Linear information by Erich Novak

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

Description

Multivariate problems occur in many applications. These problems are defined on spaces of $d$-variate functions and $d$ can be huge--in the hundreds or even in the thousands. Some high-dimensional problems can be solved efficiently to within $\varepsilon$, i.e., the cost increases polynomially in $\varepsilon^{-1}$ and $d$. However, there are many multivariate problems for which even the minimal cost increases exponentially in $d$. This exponential dependence on $d$ is called intractability or the curse of dimensionality. This is the first volume of a three-volume set comprising a comprehensive study of the tractability of multivariate problems. It is devoted to tractability in the case of algorithms using linear information and develops the theory for multivariate problems in various settings: worst case, average case, randomized and probabilistic. A problem is tractable if its minimal cost is not exponential in $\varepsilon^{-1}$ and $d$. There are various notions of tractability, depending on how we measure the lack of exponential dependence. For example, a problem is polynomially tractable if its minimal cost is polynomial in $\varepsilon^{-1}$ and $d$. The study of tractability was initiated about 15 years ago. This is the first and only research monograph on this subject. Many multivariate problems suffer from the curse of dimensionality when they are defined over classical (unweighted) spaces. In this case, all variables and groups of variables play the same role, which causes the minimal cost to be exponential in $d$. But many practically important problems are solved today for huge $d$ in a reasonable time. One of the most intriguing challenges of the theory is to understand why this is possible. Multivariate problems may become weakly tractable, polynomially tractable or even strongly polynomially tractable if they are defined over weighted spaces with properly decaying weights. One of the main purposes of this book is to study weighted spaces and obtain necessary and sufficient conditions on weights for various notions of tractability. The book is of interest for researchers working in computational mathematics, especially in approximation of high-dimensional problems. It may be also suitable for graduate courses and seminars. The text concludes with a list of thirty open problems that can be good candidates for future tractability research.

How long is Tractability of Multivariate Problems: Linear information?

Tractability of Multivariate Problems: Linear information by Erich Novak is 402 pages long, and a total of 101,304 words.

This makes it 136% the length of the average book. It also has 124% more words than the average book.

How Long Does it Take to Read Tractability of Multivariate Problems: Linear information Aloud?

The average oral reading speed is 183 words per minute. This means it takes 9 hours and 13 minutes to read Tractability of Multivariate Problems: Linear information aloud.

What Reading Level is Tractability of Multivariate Problems: Linear information?

Tractability of Multivariate Problems: Linear information 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: Linear information?

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