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Titlebook: Optimal Estimation in Approximation Theory; Charles A. Micchelli,Theodore J. Rivlin (Symposium Book 1977 Springer Science+Business Media N

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书目名称Optimal Estimation in Approximation Theory
编辑Charles A. Micchelli,Theodore J. Rivlin (Symposium
视频video
丛书名称The IBM Research Symposia Series
图书封面Titlebook: Optimal Estimation in Approximation Theory;  Charles A. Micchelli,Theodore J. Rivlin (Symposium Book 1977 Springer Science+Business Media N
描述The papers in this volume were presented at an International Symposium on Optimal Estimation in Approximation Theory which was held in Freudenstadt, Federal Republic of Germany, September 27-29, 1976. The symposium was sponsored by the IBM World Trade Europe/Middle East/Africa Corporation, Paris, and IBM Germany. On behalf of all the participants we wish to express our appreciation to the spon­ sors for their generous support. In the past few years the quantification of the notion of com­ plexity for various important computational procedures (e. g. multi­ plication of numbers or matrices) has been widely studied. Some such concepts are necessary ingredients in the quest for optimal, or nearly optimal, algorithms. The purpose of this symposium was to present recent results of similar character in the field or ap­ proximation theory, as well as to describe the algorithms currently being used in important areas of application of approximation theory such as: crystallography, data transmission systems, cartography, reconstruction from x-rays, planning of radiation treatment, optical perception, analysis of decay processes and inertial navigation system control. It was the hope of the
出版日期Book 1977
关键词Approximation; algorithms; approximation theory; character; computation; construction; control; data transm
版次1
doihttps://doi.org/10.1007/978-1-4684-2388-4
isbn_softcover978-1-4684-2390-7
isbn_ebook978-1-4684-2388-4
copyrightSpringer Science+Business Media New York 1977
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Minimal Projections,n of Y is finite. When dim Y<∞ there is always a minimal element in A but codim Y<∞ does not imply this conclusion (see [3]). We will discuss the problem of characterizing minimal element in A or in some proper subset. This problem is trivial when X is an Hilbert space or Y is 1-dimensional.
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Interpolation Operators as Optimal Recovery Schemes for Classes of Analytic Functions,or |α − f.(x)| is at least as large as |α. − f(x)|. If moreover a function s. ∈ ℬ can be found such that s. evaluated at x gives the optimal value α. and this is so for every x in the domain of the functions f then s. is considered an . (or extrapolant) for these functions.
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Estimation Problems in Data-Transmission Systems,owly over time. A second set of problems deals with recovering the transmitted information from received noisy signals. It is shown that in the presence of severe signal distortion and/or redundant sequence coding the optimum receiver has to solve a dynamic programming problem.
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Optimal State Estimation and its Application to Inertial Navigation System Control, in a noisy environment the considerations about the estimator design are extended to the design of simple, (sub-) optimal controllers. A comparison to the optimal estimation accuracy shows the efficiency of proposed output feedback controller design procedure in this technical example.
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Estimation Problems in Crystallography,ith a set of estimates which fit into the noise limits of the data, as is shown by a series of test examples. A reduction of the number of possible estimates can be made by introducing additional restrictions involving more crystallographic information. The purpose of this contribution is not to giv
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