Geodesic
The problem of moments on a finite set of points
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 6 (2003) no. 2, pp. 149-157 Cet article a éte moissonné depuis la source Math-Net.Ru

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The influence of the last diagonal entry $b_n$ of the Jacobi matrix on its eigenvalues, which at the same time are the nodes of orthogonality of respective polynomials as well as on the squares of the first components of the normalized eigenvectors – the weights of the orthogonality, is considered. The weights of orthogonality are the distribution masses whose moments are known and given by the positive definite Hankel matrix independent of $b_n$. Using the solutions to the equations with special matrices the first derivatives of $b_n$ of the nodes and the weights of orthogonality of the polynomials are calculated. Their asymptotic behavior with $b_n\to\pm\infty$ is discussed. 
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     title = {The problem of moments on a~finite set of points},
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Yu. I. Kuznetsov. The problem of moments on a finite set of points. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 6 (2003) no. 2, pp. 149-157. http://geodesic.mathdoc.fr/item/SJVM_2003_6_2_a4/

[1] Akhiezer Yu. I., Klassicheskaya problema momentov, Fizmatgiz, M., 1961

[2] Krein M. G., Nudelman A. A., Problema momentov Markova i ekstremalnye zadachi, Nauka, M., 1973 | MR

[3] Kuznetsov Yu. I., Elementy analiza na konechnom mnozhestve tochek, Izd-vo VTs SO RAN, Novosibirsk, 1994 | MR

[4] Ilin V. P., Kuznetsov Yu. I., Algebraicheskie osnovy chislennogo analiza, Nauka, Novosibirsk, 1986 | MR

[5] Kuznetsov Yu. I., “Matrichno-mnogochlennye struktury v konechnomernom lineinom vektornom prostranstve”, Sib. mat. zhurn., 42:4 (2001), 815–824 | MR | Zbl

[6] Golub Dzh., Van Loun Ch., Matrichnye vychisleniya, Mir, M., 1999