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Editorial Board       p-ISSN 2308-4944 (print)       e-ISSN 2409-0085 (online)
SOI: 1.1/TAS         DOI: 10.15863/TAS

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ISJ Theoretical & Applied Science 12(68) 2018

Philadelphia, USA

* Scientific Article * Impact Factor 6.630

Zhanatauov, S. U.

Inverse spectral problem.

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Language: Russian

Citation: Zhanatauov, S. U. (2018). Inverse spectral problem. ISJ Theoretical & Applied Science, 12 (68), 101-112. Soi: Doi:

Pages: 101-112

Published: 30.12.2018

Abstract: The article solved a new spectral problem - ISP 3, inverse to the Direct Spectral Problem [3]. For known values of the eigenvalues ?1,…,??, such that ?1>…>??>0, ??+?+1>…>?+n>0, ?1+?2+??+?+?+1+…+?+n=n, ?+nn=diag(?1,?2,??,?+?+1,…,?+n); 3) ?+nn=diag(?1,?2,??,?+?+1,…,?+n) should have the given values of f-parameters f1(?+nn)=?1+…+?n)=f1, f2(?+nn)=(?21+…+?+2n)=f2, f3(?+nn)=?1/?+n=f3, 1-f4(?+nn)=(?1+…+??)/n=1-f4, f5(?+nn)=?1??2????…??+n= f5, f6(?+66)=?1/?2+…+?+n-1/?+n)=f6; 4) the matrices C+nn and ?+nn satisfy the relations from DSP. With the use of ISP 3, a new algorithm has been developed for estimating missing non-dominant eigenvalues. An example is given when n = 6 estimates of the missing non-dominant eigenvalues of the unknown correlation matrix of 20 real measurements of 6 properties of a cereal crop.

Key words: inverse, spectral, problem.








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