Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Parameter identifiability under approximation

Authors: K. Kunisch and L. W. White
Journal: Quart. Appl. Math. 44 (1986), 475-486
MSC: Primary 49D15; Secondary 93B30, 93C05
DOI: https://doi.org/10.1090/qam/860900
MathSciNet review: 860900
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Abstract: The problem of injectivity of the parameter-to-state map is discussed for Galerkin approximations of a linear parabolic equation. A necessary and sufficient condition is derived and illustrated by means of simple examples. Finally, output least squares identifiability of the Galerkin approximations is discussed.

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  • [1] A. Bamberger, G. Chavent, and P. Lailly, About the stability of the inverse problem in a 1-D wave equation--application to the interpretation of seismic profiles, J. Appl. Math. Optim. 5, 1-47 (1979) MR 526426
  • [2] H. T. Banks and P. L. Daniel, Estimation of variable coefficients in parabolic systems, LCDS Report 82-22, Brown University, Sept. 1982; IEEE Trans. Autom. Control. 30, 386-398 (1985)
  • [3] H. T. Banks and K. Kunisch, An approximation theory for nonlinear partial differential equations with applications to identification and control, SIAM J. Control Optimization 20, 815-849 (1982) MR 675572
  • [4] G. Chavent, Local stability of the output least square parameter estimation technique, INRIA Report No. 136, Paris (1982); Mat. Apl. Comput. 2, 3-22 (1983) MR 699367
  • [5] I. M. Gelfand and B. M. Levitan, On the determination of a differential equation from its spectral function, Am. Math. Soc. Transl. 1, 253-304 (1955) MR 0073805
  • [6] T. Kato, Perturbation theory for linear operators, Springer, New York, 1966 MR 0203473
  • [7] S. Kitamura and S. Nakagiri, Identifiability of spatially varying and constant parameters in distributed systems of parabolic type, SIAM J. Control Optimization 15, 785-802 (1979) MR 0459856
  • [8] K. Kunisch and L. W. White, The parameter estimation problem for parabolic equations and discontinuous observation operators, SIAM J. Control Optimization 23, 900-927 (1985) MR 809541
  • [9] A. Pierce, Unique identification of eigenvalues and coefficients in a parabolic problem, SIAM J. Control Optimization 17, 494-499 (1979) MR 534419
  • [10] T. Suzuki, Uniqueness and nonuniqueness in an inverse problem for the parabolic equation, J. Differ. Eq. 47, 296-316 (1983) MR 688107
  • [11] L. W. White, Identification of a friction parameter in a first order linear hyperbolic equation, Proc. 22nd IEEE Conf. Decision and Control, San Antonio, 56-59 (1983)
  • [12] A. E. Taylor and D. C. Lay, Introduction to functional analysis, Wiley, New York, 1980 MR 564653

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DOI: https://doi.org/10.1090/qam/860900
Article copyright: © Copyright 1986 American Mathematical Society

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