References
- [1] J. Abaffy, E. Spedicato: ABS Projections Algorithms Mathematical Techniques for Linear and Nonlinear Algebraic Equations, Ellis Horwood Ltd, Chichester, England, (1989)
- [2] J. Abaffy M. Bertocchi, A.Torriero c Perturbations of M-matrices via ABS methods and their applications to input-output analysis Applied Mathematics and Computation Vol. 94 145 170 (1998)
- [3] J. Abaffy, Sz. Fodor: Reortogonalization methods in ABS classes, Acta Polytechnica Hungarica Vol 12 No 6 pp. 23-41 (2015)
- [4] J. Abaffy, E. Feng, A. Galántai: Introduction to ABS methods for equations and Optimization Part I. Saarbrücken (Germany) : GlobeEdit 131 pages (2017)
- [5] J. Abaffy, Sz. Fodor: ABS-Based Direct Method for Solving Complex Systems of Linear Equations Mathematics 9 : 19 p. 2527 (2021)
- [6] Anderson, E., Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK User’s Guide (http://www.netlib.org/lapack/lug/la-pack_lug.html), Third Edition, SIAM, Philadelphia, (1999).
- [7] W. E. Arnoldi., The principle of minimized iteration in the solution of the matrix eigenvalue problem, Quart. Appl. Math., 9 pp. 17-29. (1951)
- [8] Jesse L. Barlow, Reorthogonalization for the Golub–Kahan–Lanczos bidiagonal reduction, Numer. Math. 124:237–278 DOI 10.1007/s00211-013-0518-8 (2013)
- [9] W. Daniel, W. B. Gragg, L. Kaufman and G. W. Stewart Reorthogonalization and Stable Algorithms for Updating the Gram-Schmidt QR Factorization, Math. of Comput., Vol 30, No. 136 pp. 772-795 (1976)
- [10] A. Galántai, Cs. J. Heged¶s: Hyman’s method revisited, J. of Comput. and Applied Math. Vol 226 pp. 246-258 (2009)
- [11] H. Golub, C.F. Van Loan: Matrix computation, North Oxford Academic Press, Oxford (1983)
- [12] Cs. J. Heged¶s: Reorthogonalization Methods Revisited Ata Polytechnica Hungarica 12 : 8 pp. 7-28. (2015)
- [13] W. Heisenberg: Die beobachtbaren Grössen in der Theorie der Elementarteilchen. I Z. Phys. 120 (7–10):pp. 513–538. (1943)
- [14] W. Heisenberg: Die beobachtbaren Größen in der Theorie der Elementarteilchen. II Z. Phys 120, pp 673–702 (1943
- [15] W. Heisenberg: Die beobachtbaren Größen in der Theorie der Elementarteilchen. III Z. Phys. 123, pp. 93–112 (1944)
- [16] D.L. Karney, R T. Gregory: A collection of matrices for testing computational algorithms Wiley pp 163 (1969)
- [17] W.W. Leontief. „An Alternative to Aggregation in Input-Output Analysis and National Accounts”. Review of Economics and Statistics. 49 (3): 412–419. (1967) doi: 10.2307/1926651. JSTOR 1926651
- [18] N. Parlett, The Symmetric Eigenvalue Problem, Prentice-Hall, Inc., Englewood Cli s, N.J. 07632. ISBN 0-13-880047-2.(1980),
- [19] Y. Saad, Variations on Arnoldi’s method for computing eigenelements of large unsymmetric matrices, Lin. Alg. Appl., Vol. 34, pp. 269-295. (1980)
- [20] Y. Saad and M. H. Schultz: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems, SIAM J. ScI. Stat. Comput Vo|. 7, No. 3, pp 856-869 July (1986) Read More-https://epubs.siam.org/doi/abs/10.1137/0907058
- [21] G. W. Stewart, Matrix Algorithms II: Eigensystems, SIAM, Vol. II. (2001)
- [22] O. S. Vaidya and S. Kumarb, Analytic hierarchy process: An overview of applications, European Journal of Operational Research Vol. 169, No-1 pp. 1-29 (2006)
- [23] D. S. Watkins: The Matrix Eigenvalue Problem, Society for Industrial and Applied Mathematics 451 pages (2007)
- [24] J. H. Wilkinson Convergence of the LR, QR, and related algorithms, The Computer Journal, pp 77-84 (1965,)
- [25] J.H. Wilkinson: Algebraic eigenvalue problem Oxford University Press, 683 pages (1965)