Full Article: PDF
Scientific Object Identifier: http://s-o-i.org/1.1/TAS-12-68-19
DOI: https://dx.doi.org/10.15863/TAS.2018.12.68.19
Language: Russian
Citation: Zhanatauov, S. U. (2018). Inverse spectral problem. ISJ Theoretical & Applied Science, 12 (68), 101-112. Soi: http://s-o-i.org/1.1/TAS-12-68-19 Doi: https://dx.doi.org/10.15863/TAS.2018.12.68.19 |
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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