A Newton–Kantorovich Method in Inverse Source Problems for Production-Destruction Models with Time Series-Type Measurement Data

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A Newton–Kantorovich Method in Inverse Source Problems for Production-Destruction Models with Time Series-Type Measurement Data. / Penenko, A. V.

в: Numerical Analysis and Applications, Том 12, № 1, 01.01.2019, стр. 51-69.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{34650b22f2894803baf4cb39803e211f,

title = "A Newton–Kantorovich Method in Inverse Source Problems for Production-Destruction Models with Time Series-Type Measurement Data",

abstract = "Algorithms for solving an inverse source problem for production–destruction systems of nonlinear ordinary differential equations with measurement data in the form of time series are presented. A sensitivity operator and its discrete analogue are constructed on the basis of adjoint equations. This operator relates perturbations of the sought-for parameters of the model to those of the measured values. The operator generates a family of quasi-linear operator equations linking the required unknown parameters and the data of the inverse problem. A Newton–Kantorovich method with right-hand side r-pseudo-inverse matrices is used to solve the equations. The algorithm is applied to solving an inverse source problem for an atmospheric pollution transformation model.",

keywords = "adjoint equations, big data, inverse source problem, Newton–Kantorovich method, r-pseudoinverse matrix, right inverse, sensitivity operator",

author = "Penenko, {A. V.}",

note = "Publisher Copyright: {\textcopyright} 2019, Pleiades Publishing, Ltd.",

year = "2019",

month = jan,

day = "1",

doi = "10.1134/S1995423919010051",

language = "English",

volume = "12",

pages = "51--69",

journal = "Numerical Analysis and Applications",

issn = "1995-4239",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "1",

}

RIS

TY - JOUR

T1 - A Newton–Kantorovich Method in Inverse Source Problems for Production-Destruction Models with Time Series-Type Measurement Data

AU - Penenko, A. V.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Algorithms for solving an inverse source problem for production–destruction systems of nonlinear ordinary differential equations with measurement data in the form of time series are presented. A sensitivity operator and its discrete analogue are constructed on the basis of adjoint equations. This operator relates perturbations of the sought-for parameters of the model to those of the measured values. The operator generates a family of quasi-linear operator equations linking the required unknown parameters and the data of the inverse problem. A Newton–Kantorovich method with right-hand side r-pseudo-inverse matrices is used to solve the equations. The algorithm is applied to solving an inverse source problem for an atmospheric pollution transformation model.

AB - Algorithms for solving an inverse source problem for production–destruction systems of nonlinear ordinary differential equations with measurement data in the form of time series are presented. A sensitivity operator and its discrete analogue are constructed on the basis of adjoint equations. This operator relates perturbations of the sought-for parameters of the model to those of the measured values. The operator generates a family of quasi-linear operator equations linking the required unknown parameters and the data of the inverse problem. A Newton–Kantorovich method with right-hand side r-pseudo-inverse matrices is used to solve the equations. The algorithm is applied to solving an inverse source problem for an atmospheric pollution transformation model.

KW - adjoint equations

KW - big data

KW - inverse source problem

KW - Newton–Kantorovich method

KW - r-pseudoinverse matrix

KW - right inverse

KW - sensitivity operator

UR - http://www.scopus.com/inward/record.url?scp=85064040339&partnerID=8YFLogxK

U2 - 10.1134/S1995423919010051

DO - 10.1134/S1995423919010051

M3 - Article

AN - SCOPUS:85064040339

VL - 12

SP - 51

EP - 69

JO - Numerical Analysis and Applications

JF - Numerical Analysis and Applications

SN - 1995-4239

IS - 1

ER -

ID: 19358591