Algebraic description of the finite Stieltjes moment problem
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10393271" target="_blank" >RIV/00216208:11320/19:10393271 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=jQtjsnYoiQ" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=jQtjsnYoiQ</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.laa.2018.09.026" target="_blank" >10.1016/j.laa.2018.09.026</a>
Alternative languages
Result language
angličtina
Original language name
Algebraic description of the finite Stieltjes moment problem
Original language description
The Stieltjes problem of moments seeks for a nondecreasing positive distribution function mu(lambda) on the semi-axis [0, +infinity) so that its moments match a given infinite sequence of positive real numbers m(0), m(l), . . . . In his seminal paper Investigations on continued fractions published in 1894 Stieltjes gave a complete solution including the conditions for the existence and uniqueness in relation to his main goal, the convergence theory of continued fractions. One can also reformulate the Stieltjes problem of moments as looking for a sequence of positive distribution functions mu((1))(lambda), mu((2))(lambda), . . . , where the nth distribution function has n points of increase and, m(0), m(1), . . . , m(2n-1 )represent its (first) 2n moments, i.e., as the sequence of the finite Stieltjes moment problems. This view can be linked to iterative solution of (large) linear algebraic systems. Providing that m(0), m(1), . . . , are moments of some linear, self-adjoint and coercive operator A on a Hilbert space with respect to a given vector f , the finite Stieltjes moment problems determine the iterations of the conjugate gradient method applied for solving Au = f, and vice versa. Here the existence and uniqueness is guaranteed by the properties of the operator A (reformulation for finite sequences, matrices and finite vectors is obvious). This fundamental link raises a question on how the solution of the finite Stieltjes moment problem can be described purely algebraically. This has motivated the presented exposition built upon ideas published previously by several authors. Since the description uses matrices of moments, it is not intended for numerical computations. (C) 2018 Elsevier Inc. All rights reserved.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA18-12719S" target="_blank" >GA18-12719S: Thermodynamical and mathematical analysis of flows of complex fluids</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Linear Algebra and Its Applications
ISSN
0024-3795
e-ISSN
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Volume of the periodical
561
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
21
Pages from-to
207-227
UT code for WoS article
000450385500012
EID of the result in the Scopus database
2-s2.0-85054323631