An approximate inverse matrix technique for arrowhead matrices

International Journal of Computer Mathematics

Volumn 70, Issue 1, 1998, Pages 35-45

  Gravvanis, George A ^a,b  

^a Nursing Military Academy   (Greece)

^b TECHNICAL UNIVERSITY OF CRETE   (Greece)

Author keywords

Approximate factorization procedures; Approximate inverse matrix techniques; Arrowhead matrix; Bordered diagonal matrix; Preconditioning

Indexed keywords

FACTORIZATION; INVERSE PROBLEMS; ITERATIVE METHODS; LINEAR SYSTEMS; NUMERICAL METHODS;

APPROXIMATE FACTORIZATION; APPROXIMATE INVERSE; DIAGONAL MATRICES; ITERATIVE SCHEMES; NUMERICAL RESULTS; PRECONDITIONING; SOLUTION OF LINEAR SYSTEMS;

MATRIX ALGEBRA;

EID: 0002398607     PISSN: 00207160     EISSN: None     Source Type: Journal    
DOI: 10.1080/00207169808804734     Document Type: Article

References (21)

1. Arbenz, P. and Golub, G. H. (1992). QR-like algorithms for symmetric arrow matrices, SIAM J. Matrix Anal. Appl., 13, 655-658.
2. Cuppen, J. J. H. (1981). A divide and conquer method for the symmetric tridiagonal eigenproblem, Numer. Math., 36, 177-195.
3. Dongarra, J. J., Duff, I. S., Sorensen, D. C. and Van der Vorst, H. A (1991). Solving Linear Systems on Vector and Shared Memory Computers, SIAM, Philadelphia.
4. Duff, I. S., Erisman, A. M. and Reid, J. K. (1986) Direct Methods for Sparse Matrices, Oxford University Press, London.
5. Evans, D. J. (1985). Iterative methods for sparse systems, In: Sparsity and its Applications, D. J. Evans, Ed., Cambridge University Press, Cambridge
6. Evans, D J. and Sutti, C. (1988). Parallel Computing: Methods, Algorithms and Applications, Proceedings of the International Meeting on Parallel Computing, Adam Hilger.
7. Golub, G. H. (1973). Some modified matrix eigenvalue problems, SIAM Review, 15, 318-334.
8. Golub, G. H. and van Loan, C. (1989). Matrix Computations, Second edition, The Johns Hopkins University Press.
9. Gragg, B. and Harrod, W. (1984). The numerically stable reconstruction of Jacobi matrix from spectral data, Numer. Math., 44, 317-355.
10. Gravvanis, G. A. (1995). Explicit preconditioned methods for solving 3D boundary value problems by approximate inverse finite element matrix techniques, I. J. Comp. Math., 56, 77-93.
11. Gravvanis, G. A. (1996) The rate of convergence of explicit approximate inverse preconditioning, I. J. Comp. Math., 60, 77-89.
12. Gravvanis, G. A. and Lipitakis, E. A. (1992). A class of explicit preconditioned conjugate gradient methods for solving large finite element system, I. J. Comp. Math., 44, 189-206.
13. Gravvanis, G. A. and Lipitakis, E. A. (1996). An explicit sparse unsymmetric finite element solveer, Commun. Numer. Math. in Engin., 12, 21-29.
14. Gravvanis, G. A. and Lipitakis, E. A. (1996). A three dimensional explicit preconditioned solver, I. J. Comp. Math. with Appl., 32, 111-131.
15. O'Leary, D. and Stewart, G. (1990). Computing the eigenproblem and eigenvectors of arrowhead matrices, J. Comp. Physics, 90, 497-505.
16. Ortega, J. M. (1988). Introduction to parallel and vector solution of linear systems, In Series: Frontiers of Computer Science, A. L. Rosenberg, Ed., Plenum Press, N. Y.
17. Parlett, B. (1980). The Symmetric Eigenvalue Problem, Prentice-Hall, Enlewood Cliffs, NJ.
18. Parlett, B. and Nour-Omid, B. (1985). The use of refined error bound when updating eigenvalues of tridiagonals, Lin. Alg. Appl., 68, 179-219.
19. Rutishauser, H. (1963). On Jacobi rotation patterns, In: Experimental Arithmetic, High Speed Computing and Mathematics, Proceedings of the symposium on Applied Mathematics, Vol. 15, AMS, Providence pp. 219-239.
20. Wilkinson, J. H. (1965). The Algebraic Eigenvalue Problem, Clarendon Press, Oxford.
21. Zha, H. (1992). A two-way chasing scheme for reducing a symmetric arrowhead matrix to tridiagonal form, J. Numer. Alg. Appl., 1, 49-57.