Vol. 6, №1, 2014
РусскийEnglish
BRIEF REPORTS
EXTREMELY SPARSE MATRICES
Evtikhov M. G.
Kotel’nikov Institute of Radio-Engineering and Electronics, Fryazino Branch, Russian Academy of Science, http://fire.relarn.ru
1, Vvedensky sq., 141120 Fryazino, Moscow region, Russian Federation,
emg2002@mail.ru
Jacobi Matrix for a system of dozens (hundreds) of the nonlinear equations is built with the use of the proposed concept is extremely sparse matrices. Knowledge of algebraic properties of such matrices allows to prove the obvious theorem on matrices. Efficient algorithms for computation of matrices of Jacobi important when building a gradient of numerical methods, for example, Newton’s method for solving systems of nonlinear equations.
Keywords : matrix theory, gradient calculation methods, Newton's method of solving a system of nonlinear algebraic equations.
UDC 519.615.5
Bibliography- 4 references
Received 18.05.2011
RENSIT, 2011, 3(1):97-101
REFERENCES
- Tewarson RP. Sparse Matrices. NY, Acad. Press, 1973.
- Bakhvalov NS, Zhidkov NP, Kobelkov GM. Chislennye metody [Numerical methods]. Moscow, Lab.bazovykh znaniy Publ., 2002, 632 p.
- Gantmakher FR. Teoriya matrits [Theory of matrices]. Moscow, Nauka Publ., 1966, 576 p.
- Voevodin VV, Kuznetsov YuA. Matritsy i vychisleniya [Matrices and computation]. Moscow, Nauka Publ., 1984,320 p.