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INVERSE SPECTRAL PROBLEM
Authors: Sapargali Zhanatauov
Number of views: 325
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