Theories of Computational Complexity

Ivan V. Sergienko (), Valeriy K. Zadiraka () and Oleg M. Lytvyn ()
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Ivan V. Sergienko: National Academy of Sciences of Ukraine
Valeriy K. Zadiraka: National Academy of Sciences
Oleg M. Lytvyn: Ukrainian Engineering Pedagogics Academy

Chapter Chapter 2 in Elements of the General Theory of Optimal Algorithms, 2021, pp 29-73 from Springer

Abstract: Abstract This chapter is devoted to the issues of algebraic and analytical computational complexity of problem solving. The main focus is on computer technology for computational processes, which is covered for various computational models. An important reserve for computational optimization is the construction and use of optimal in accuracy and speed computational algorithms. This allows you to solve the problem with the least error and can transfer the problem from the class of unsolvable problems to the class of solvable ones. The choice of information solution operator is also a reserve for computational optimization. Successful choice of the information operator makes it possible to reduce the Chebyshev radius of the uncertainty region of the approximate solution of the problem. These approaches are illustrated by the problem of approximate calculation of integrals from fast-oscillating functions in both one-dimensional and multidimensional cases.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-90908-6_2

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DOI: 10.1007/978-3-030-90908-6_2

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