A numerucal numerical method for the restoration of the five diagonal symmetric matrices from the spectral data
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Keywords:
differential equations, band matrix, spectral problems, eigenvalues, five-diagonal symmetric matrix.Abstract
In this work the possibility of restoration of real symmetrical five diagonal final matrixes using four numerically sequences is studied. Three from these four numerically sequences are interpreted as sets of eigenvalues of the considered matrix and else of two matrixes, obtained from considered matrix delet-ing some diagonal elements. The concrete formulas of construction of matrix elements using four sets of eigenvalues are obtained.References
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3. Godunov S.K., Kostin V.I., Mitchenko A.D. Vychislenie sobstvennogo vektora simmetricheskoj trehdiagonal'noj matricy // Sib. mat. zhurnal, –
1985. – T. 26. – № 5. – P.71-85.
4. Godunov S.K. Sovremennye aspekty linejnoj algebry,– Novosibirsk: Nauchnaja kniga, 1997,– P.390.
5. Voevodin V.V. Chislennye metody algebry. Teorija i algorifmy. – M.: Nauka, 1966. – 235 s.
6. Uilkinson Dzh. X. Algebraicheskaja problema sobstvennyh znachenij. – M.: Nauka, 1970. – 108 s.
7. Danilina N.I., Dubrovskaja N.S., Kvasha O.P., Smirnov G.L., Fekansov G.I. Chislennye metody. – M.: Vysshaja shkola, 1976. – P.368.
8. Matematicheskij jenciklopedicheskij slovar, – M.: Sovetskaja jenciklopedija, 1988. – P.847.
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12. Ikramov H.D. Chislennye metody linejnoj algebry. (Reshenie linejnyh uravnenij). – M.: Znanie, 1987. – P.241.
13. Markus M., Mink H. Obzor po teori matric i matrichnyh neravenstv. – M.: Nauka, 1972. – P. 34. 14. Ikramov H.D. Chislennye metody dlja simmetrichnyh linejnyh sistem. – M.: Nauka, 1988. – P.102.
15. Ikramov H.D. Vychislitel'nye metody linejnoj algebry. (Reshenie bol'shih razrezhennyh sistem uravnenij prjamymi metodami), – M.: Znanie. – 1989. – P.84.
16. Parlett B. Simmetrichnaja problema sobstvennyh znachenij. – M.: Mir, 1983. – P.76.
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Eleuov, A. A., Tungatarov, N. N., & Yakhiyayev, F. K. (2015). A numerucal numerical method for the restoration of the five diagonal symmetric matrices from the spectral data. International Journal of Mathematics and Physics, 6(1), 33–41. Retrieved from https://ijmph.kaznu.kz/index.php/kaznu/article/view/115
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Astronomy and Space Research
