Numerical Analysis and Applications

, Volume 12, Issue 1, pp 51–69 | Cite as

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

  • A. V. PenenkoEmail author


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.


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


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Institute of Computational Mathematics and Mathematical Geophysics, Siberian BranchRussian Academy of SciencesNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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