A new modification of the Rojo method for solving symmetric circulant five-diagonal systems of linear equations

Computers and Mathematics with Applications

Volumn 35, Issue 10, 1998, Pages 35-44

  El Sayed, S M ^a   Ivanov, I G ^b   Petkov, M G ^b  

^a BENHA UNIVERSITY   (Egypt)

^b SHUMEN UNIVERSITY   (Bulgaria)

Author keywords

Circulant linear system; Diagonal dominant matrix; Five diagonal circulant matrix; Toeplitz matrix; Woodbury formula

Indexed keywords

APPROXIMATION THEORY; LINEAR EQUATIONS; MATRIX ALGEBRA; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

CIRCULANT LINEAR SYSTEM; DIAGONAL DOMINANT MATRIX; FIVE DIAGONAL CIRCULANT MATRIX; ROJO METHOD; TOEPLITZ MATRIX; WOODBURY FORMULA;

MATHEMATICAL TECHNIQUES;

EID: 0032066988     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(98)00070-4     Document Type: Article

References (12)

1. O. Rojo, A new method for solving symmetric circulant tridiagonal systems of linear systems, Computers Math. Applic. 20 (12), 61-67, (1990).
2. B.L. Buzbee, G.H. Golub and C.W. Nielson, On direct methods for solving Poisson's equations, SIAM J. Numer. Analysis 7, 627-656, (1970).
3. D. Fischer, G. Golub, O. Hald, C. Leiva and O. Widlund, On Fourier-Toeplitz methods for separable elliptic problems, Math. Comput. 28, 349-368, (1974).
4. C. Mingkui, On the solution of circulant linear systems, SIAM Jl. Numer. Analysis 24, 668-683, (1987).
5. U. Zavyalov, B. Kvasov and V. Miroshnichenko, Spline Functions Methods, (in Russian), Moscow, (1980).
6. A.S. Housholder, The Theory of Matrices in Numerical Analysis, Blaisdell, New York, (1964).
7. R.F. Boisvert, Algorithms for special tridiagonal systems, SIAM J. Sci. Stat. Comput. 12, 423-442, (1991).
8. V. Voevodin and E. Tyrtyshnikov, Computations with Toeplitz matrices, In Computational Processes and Systems, (in Russian), Volume 1, pp. 124-266, Moscow, (1983).
9. D.J. Evans, On the solution of certain Toeplitz tridiagonal linear systems, SIAM J. Numer. Anal. 17, 675-680, (1980).
10. R.F. Boisvert, A fourth-order accurate Fourier method for the Helmholtz equation in three dimensions, ACM Trans. Math. Software 13, 221-234, (1987).
11. ∞, Linear Algebra Appl. 14, 211-217, (1976).
12. M.S. El-Sayed, The study on special matrices and numerical methods for special matrix equations, Ph.D. Thesis, Sofia, (1996).