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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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • 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

  • 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