Guaranteed Estimation Problems In The Theory Of Linear Ordinary Differential Equations With Uncertain Data
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Guaranteed Estimation Problems in the Theory of Linear Ordinary Differential Equations with Uncertain Data
This monograph is devoted to the construction of optimal estimates of values of linear functionals on solutions to Cauchy and two-point boundary value problems for systems of linear first-order ordinary differential equations, from indirect observations which are linear transformations of the same solutions perturbed by additive random noises. It is assumed that right-hand sides of equations and boundary data as well as statistical characteristics of random noises in observations are not known and belong to certain given sets in corresponding functional spaces. This leads to the necessity of introducing the minimax statement of an estimation problem when optimal estimates are defined as linear, with respect to observations, estimates for which the maximum of mean square error of estimation taken over the above-mentioned sets attains minimal value. Such estimates are called minimax or guaranteed estimates. It is established that these estimates are expressed explicitly via solutions to some uniquely solvable linear systems of ordinary differential equations of the special type. The authors apply these results for obtaining the optimal estimates of solutions from indirect noisy observations. Similar estimation problems for solutions of boundary value problems for linear differential equations of order n with general boundary conditions are considered. The authors also elaborate guaranteed estimation methods under incomplete data of unknown right-hand sides of equations and boundary data and obtain representations for the corresponding guaranteed estimates. In all the cases estimation errors are determined.
System Analysis & Intelligent Computing
The book contains the newest advances related to research and development of complex intellectual systems of various nature, acting under conditions of uncertainty and multifactor risks, intelligent systems for decision-making, high performance computing, state-of-the-art information technologies for needs of science, industry, economy, and environment. The most important problems of sustainable development and global threats estimation, forecast and foresight in tasks of planning and strategic decision-making are investigated. This monograph will be useful to researchers, post-graduates, and advanced students specializing in system analysis, decision-making, strategic planning or engineering design, fundamentals of computational Intelligence, artificial Intelligence systems based on hybrid neural networks, big data, and data mining.
Inverse Problems and Large-Scale Computations
Author: Larisa Beilina
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-10-01
This volume is a result of two international workshops, namely the Second Annual Workshop on Inverse Problems and the Workshop on Large-Scale Modeling, held jointly in Sunne, Sweden from May 1-6 2012. The subject of the inverse problems workshop was to present new analytical developments and new numerical methods for solutions of inverse problems. The objective of the large-scale modeling workshop was to identify large-scale problems arising in various fields of science and technology and covering all possible applications, with a particular focus on urgent problems in theoretical and applied electromagnetics. The workshops brought together scholars, professionals, mathematicians, and programmers and specialists working in large-scale modeling problems. The contributions in this volume are reflective of these themes and will be beneficial to researchers in this area.