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MATRIX ARITHMETIC BASED ON FIBONACCI MATRICES

Alexey Stakhov (Ukraine)

e-mail: anna@nest.vinnica.ua

 PDF, 314 kB

Страницы: 158-163.

Язык статьи: English.

Citation:
Stakhov A. Matrix arithmetic based on Fibonacci matrices. Computer Optics 2001; 21: 158-163.

Литература:

  1. Bashmakova, J.G., Youshkevich, A.P. "Origin of Number Systems". Encyclopedia of Elementary Mathematics. Book 1 "Arithmetic". MoscowLeningrad: Publisher "Gostekhizdat", 1951, 427 p. (In Russian).
  2. Shаnnon C. "А symmetrical notation for numbers". The American Mathematical Monthly, Vol. 57, No 2, 1950.
  3. Bergman, G. "A number system with an irrational base". Mathematics Magazine, No 31, 1957, P. 98- 119.
  4. Stakhov, A.P. The Golden Ratio Codes. Moscow: Publisher "Radio and Communication", 1984, 140 p. [In Russian].
  5. Khmelnik, S. I. "Coding of the functions". Cybernetics, No 4, 1966. P. 88-92 [In Russian].
  6. Khmelnik, S.I. "Coding of the vectors". Cybernetics, No 5, 1969. P. 54-57 [In Russian] .
  7. Khmelnik, S.I. "Coding of the plane figures". Automation and Computer Engineering, No 6, 1970. P. 17-21 [In Russian].
  8. Khmelnik, S.I. "Algebra of the multi-dimensional vectors, and coding of the space figures". Automation and Computer Engineering, No 1, 1971, pp. 15-19 [In Russian].
  9. Pospelov, D.A. Arithmetical Foundations of Digital Computers. Moscow, Publisher "Vyshaja shkola", 1970, 320 p. [In Russian].
  10. Hoggat, Verner E. Fibonacci and Lucas Numbers, California: Houghton-Mifflin, Palo Alto, 1969, 92 p.
  11. Basin, S.L. Hoggatt, V.E., Jr. "A primer on the Fibonacci sequence, Part II", The Fibonacci Quarterly, No 2, 1963, pp. 61-68.
  12. Ivie, John. "A general Q-matrix", The Fibonacci Quarterly, No.3, 1972, pp. 255-261, 264.
  13. Gould, H.W. "A history of the Fibonacci Q-matrix and a higher-dimensional problem", The Fibonacci Quarterly, No 1, 1981, pp. 250-257.
  14. Stakhov, A.P. "Application of the natural redundancy of the Fibonacci number systems for computer system control", Automation and Computer Engineering, No 6, 1975, pp. 80-87 (In Russian).
  15. Stakhov, A.P. Computer Arithmetic based on Fibonacci Numbers and Golden Section: New Information and Arithmetic Computer Foundations, Toronto, SKILLSET Training, 1997, 379 p.
  16. Chernov V.M., Pershina M.V. “FivonacciMersenne and Fibonacci-Fermat discrete transforms”. Collection of papers “The Golden Section: Theory and Applications” - Boletin de Informatica, No 9/10, 1999.

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