Informal Introduction: Data Processing, Interval Computations, and Computational Complexity
This introduction starts with material aimed mainly at those readers who axe not well familiar with interval computations and/or with the computational complexity aspects of data processing and interval computations. It provides the motivation for the basic mathematical and computational problems that we will be analyzing in this book. Readers who are well familiar with these problems can skip the bulk of this chapter and go straight to the last section that briefly outlines the structure of the book.
A typical application of this problem is: from the measurements, we know the approximate values x̃i of physical quantities xi, and we know the guaranteed accuracy Δi of each measurement. As a result, we know that xi belongs to the interval xi = [x̃i - Δi, x̃i + Δi]. We also know the algorithm f(x1,..., xn) that transforms the values xi, into the value of the desired quantity y. We want to know the set of possible values of y. For a continuous function f (x1,..., xn), this set is an interval (we will denote it by y = [y, ȳ]). So, the question is: can we compute the endpoints y and y of this interval ȳ in reasonable time?
KeywordsArithmetic Operation Interval Computation Guarantee Estimate Exact Range Metic Operation
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