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The paper considers the identifiability (i.e., the unique identification)of a composite string in the class of piecewise constant parameters.
The 1-D string vibration is measured at finitely many observation points. The observations are processed to obtain the first eigenvalue and a constant multiple of the first eigenfunction at the observation points.
It is shown that the identification by the Marching Algorithm is continuous with respect to the mean convergence in the admissible set. The result is based on the continuous dependence of eigenvalues, eigenfunctions,and the solutions on the parameters. A numerical algorithm for the identification in the presence of noise is proposed and implemented.
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참고문헌 (19)
참고문헌 신청
A. Elayyan / 1997 / On uniqueness of recovery of the discontinuous conductivity coefficient of a parabolic equation / SIAM J. Math. Anal. 28 (1) : 49 ~ 59
A. Pierce / 1979 / Unique identification of eigenvalues and coefficients in a parabolic problem / SIAM J. Control Optim. 17 (4) : 494 ~ 499
E. C. Titchmarsh / 1962 / Introduction to the theory of Fourier integrals / Oxford University Press
E. Yosida / 1980 / Functional Analysis, 6th Ed / Springer-Verlag
H. T. Banks / 1989 / Estimation techniques for distributed parameter systems / Birkhauser Boston, Inc.
A. Pierce / 1979 / Unique identification of eigenvalues and coefficients in a parabolic problem / SIAM J. Control Optim. 17 (4) : 494 ~ 499
E. C. Titchmarsh / 1962 / Introduction to the theory of Fourier integrals / Oxford University Press
E. Yosida / 1980 / Functional Analysis, 6th Ed / Springer-Verlag
H. T. Banks / 1989 / Estimation techniques for distributed parameter systems / Birkhauser Boston, Inc.
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