Research output: Contribution to journal › Article › peer-review
A Newton–Kantorovich Method in Inverse Source Problems for Production-Destruction Models with Time Series-Type Measurement Data. / Penenko, A. V.
In: Numerical Analysis and Applications, Vol. 12, No. 1, 01.01.2019, p. 51-69.Research output: Contribution to journal › Article › peer-review
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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.
N1 - Publisher Copyright: © 2019, Pleiades Publishing, Ltd.
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