Convergence and comparison results for double splittings of Hermitian positive definite matrices Article Received: 01 November 2006 Accepted: 01 January 2007 DOI:
Cite this article as: Shen, SQ., Huang, TZ. & Shao, JL. Calcolo (2007) 44: 127. doi:10.1007/s10092-007-0132-1 Abstract
For single splittings of Hermitian positive definite matrices, there are well-known convergence and comparison theorems. This paper gives new convergence and comparison results for double splittings of Hermitian positive definite matrices.
Keywords: Hermitian positive definite matrix; convergence theorem; comparison theorem; double splitting Mathematics Subject Classification (2000): 65F10 References
1. Cvetković, L.J.: Two-sweep iterative methods. Nonlinear Anal.
, 25–30 (1997)
2. Elsner, L.: Comparisons of weak regular splittings and multisplitting methods. Numer. Math.
, 283–289 (1989)
3. Golub, G.H., Varga, R.S.: Chebyshev semi-iterative methods, successive over-relaxation iterative methods, and second order Richardson iterative methods. I., II. Numer. Math.
3, 147–156, 157–168 (1961)
4. Horn, R.A., Johnson, C.R.: Matrix analysis. Cambridge: Cambridge University Press 1985
5. Miller, J.J.H.: On the location of zeros of certain classes of polynomials with applications to numerical analysis. J. Inst. Math. Appl.
, 397–406 (1971)
6. Nabben, R.: A note on comparison theorems for splittings and multisplittings of Hermitian positive definite matrices. Linear Algebra Appl.
, 67–80 (1996)
7. Ortega, J.M.: Introduction to parallel and vector solution of linear systems. New York: Plenum Press 1988
8. Shen, S.-Q., Huang, T.-Z.: Convergence and comparison theorems for double splittings of matrices. Comput. Math. Appl.
, 1751–1760 (2006)
9. Song, Y.Z.: Comparison theorems for splittings of matrices. Numer. Math.
, 563–591 (2002)
10. Varga, R.S.: Matrix iterative analysis. Englewood Cliffs, NJ: Prentice-Hall 1962
11. Woźnicki, Z.I.: Estimation of the optimum relaxation factors in partial factorization iterative methods. SIAM J. Matrix Anal. Appl.
, 59–73 (1993)
12. Woźnicki, Z.I.: Nonnegative splitting theory. Japan J. Indust. Appl. Math.
, 289–342 (1994)
13. Woźnicki, Z.I.: Basic comparison theorems for weak and weaker matrix splittings. Electron. J. Linear Algebra
, 53–59 (2001)