RECONSTRUCTIONS OF PIECEWISE CONTINUOUS AND DISCRETE FUNCTIONS USING MOMENTS

Robert M. Mnatsakanov; Rafik H. Aramyan; Farhad Jafari

doi:10.1007/s10958-024-07175-0

RECONSTRUCTIONS OF PIECEWISE CONTINUOUS AND DISCRETE FUNCTIONS USING MOMENTS

Robert M. Mnatsakanov, Rafik H. Aramyan, Farhad Jafari

Radiology

Research output: Contribution to journal › Article › peer-review

Abstract

The problem of recovering a moment-determinate multivariate function f via its moment sequence is studied. Under mild conditions on f, the point-wise and L₁-rates of convergence for the proposed constructions are established. Two cases where f is the uniform density function defined on a compact set, and f is a discrete probability mass function are investigated. Calculations of the approximants and simulation studies illustrate the behavior of the approximations in several simple examples. Analytical and simulated errors of the proposed approximations are recorded in Tables 1–5.

Original language	English (US)
Journal	Journal of Mathematical Sciences (United States)
DOIs	https://doi.org/10.1007/s10958-024-07175-0
State	Accepted/In press - 2024

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.

Keywords

Moment-recovered approximation
Rate of approximation

Publisher link

10.1007/s10958-024-07175-0

Cite this

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abstract = "The problem of recovering a moment-determinate multivariate function f via its moment sequence is studied. Under mild conditions on f, the point-wise and L1-rates of convergence for the proposed constructions are established. Two cases where f is the uniform density function defined on a compact set, and f is a discrete probability mass function are investigated. Calculations of the approximants and simulation studies illustrate the behavior of the approximations in several simple examples. Analytical and simulated errors of the proposed approximations are recorded in Tables 1–5.",

keywords = "Moment-recovered approximation, Rate of approximation",

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year = "2024",

doi = "10.1007/s10958-024-07175-0",

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journal = "Journal of Mathematical Sciences (United States)",

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AB - The problem of recovering a moment-determinate multivariate function f via its moment sequence is studied. Under mild conditions on f, the point-wise and L1-rates of convergence for the proposed constructions are established. Two cases where f is the uniform density function defined on a compact set, and f is a discrete probability mass function are investigated. Calculations of the approximants and simulation studies illustrate the behavior of the approximations in several simple examples. Analytical and simulated errors of the proposed approximations are recorded in Tables 1–5.

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KW - Rate of approximation

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ER -

RECONSTRUCTIONS OF PIECEWISE CONTINUOUS AND DISCRETE FUNCTIONS USING MOMENTS

Abstract

Bibliographical note

Keywords

Publisher link

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Cite this