Matrix-free Iterative Solution Strategies for Large Dense Linear Systems

Numerical Linear Algebra with Applications

Volumn 4, Issue 4, 1997, Pages 273-294

  Goreinov, S A ^a   Tyrtyshnikov, E E ^a   Yeremin, A Yu ^b  

^a INSTITUTE OF NUMERICAL MATHEMATICS   (Russian Federation)

^b RUSSIAN ACADEMY OF SCIENCES   (Russian Federation)

Author keywords

3D boundary integral formulations; Block low rank matrix approximations; Matrix free iterative methods; Variable block bidiagonalization algorithm

Indexed keywords

EID: 0031519338     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1506(199707/08)4:4<273::AID-NLA97>3.0.CO;2-T     Document Type: Article

References (15)

1. M. Berry. Large-scale sparse singular value computations. The Intern. J. of Supercomp. Appl., 6(1), 13-49, 1992.
2. M. Berry and A. Sameh. An overview of parallel algorithms for the singular value and dense symmetric eigenvalue problems. J. Comput. Appl. Math., 27, 191-213, 1989.
3. G. Golub and W. Kahan. Calculating the singular values and pseudo-inverse of a matrix. SIAM J. Numer. Anal., 2(3), 205-224, 1965.
4. G. Golub, F. Luk and M. Overton. A Block Lanczos method for computing the singular values and corresponding singular vectors of a matrix. ACM Transactions on Math. Soft., 7(2), 149-169, 1981.
5. G. Golub and C. Reinsch. Singular value decomposition and least squares solutions. Numer. Math., 14, 430-423, 1970.
6. S. A. Goreinov et al. Iterative solution strategies for 3D boundary integral applications. Research Report EM-RR 18/94, 1994.
7. M. R. Hackbusch and Z. P. Nowak. On the fast matrix multiplication in the boundary elements method by panel clustering. Numer. Math., 54(4), 463-491, 1989.
8. M. R. Hestenes. Inversion of matrices by biorthogonalization and related results. J. Soc. Indust. Appl. Math., 6, 51-90, 1958.
9. W. Hoffman. Iterative algorithms for Gram-Schmidt orthogonalization. Computing, 41, 335-348, 1989.
10. S. V. Myagchilov and E. E. Tyrtyshnikov. A fast matrix-vector multiplier in discrete vortex method. Russian J. Numer. Analysis and Math. Modelling, 7(4), 325-342, 1992.
11. C. C. Paige. The computation of eigenvalues and eigenvectors of very large sparse matrices. Ph. D. thesis. The University of London, 1971.
12. S. M. Rao, D. R. Wilton and A. W. Glisson Electromagnetic scattering by surfaces of arbitrary shape. IEEE Trans. on Antennas and Propag., AP-30(3), 409-418, 1982.
13. V. Rokhlin. Rapid solution of integral equations of classical potential theory. J. Comput. Physics, 60, 187-207, 1985.
14. R. R. Underwood. An iterative block Lanczos method for the solution of large sparse symmetric eigenproblems. Ph. D. thesis. Stanford University, 1975.
15. A. C. Woo, H. T. G. Wang, M. J. Schuh and M. L. Sanders. Benchmark radar targets for the validation of computational electromagnetics programs. IEEE Trans. on Antennas and Propag., 35, 84-89, 1993.