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

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7 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)51-69
Number of pages19
JournalNumerical Analysis and Applications
Volume12
Issue number1
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

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

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