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2018 | 101 | 246-252
Article title

Moore-Penrose’s inverse and solutions of linear systems

Content
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Languages of publication
EN
Abstracts
EN
We employ the generalized inverse matrix of Moore-Penrose to study the existence and uniqueness of the solutions for over- and under-determined linear systems, in harmony with the least squares method.
Year
Volume
101
Pages
246-252
Physical description
Contributors
  • ESIME-Zacatenco, Instituto Politécnico Nacional, Edif. 4, Col. Lindavista CP 07738, CDMX, México
  • ESIME-Zacatenco, Instituto Politécnico Nacional, Edif. 4, Col. Lindavista CP 07738, CDMX, México
  • ESIME-Zacatenco, Instituto Politécnico Nacional, Edif. 4, Col. Lindavista CP 07738, CDMX, México
References
  • [1] C. Lanczos, Linear systems in self-adjoint form, Amer. Math. Monthly 65(9) (1958) 665-679.
  • [2] G. Bahadur-Thapa, P. Lam-Estrada, J. López-Bonilla, On the Moore-Penrose generalized inverse matrix, World Scientific News 95 (2018) 100-110.
  • [3] C. Lanczos, Extended boundary value problems, Proc. Int. Congress Math. Edinburgh, 1958, Cambridge University Press (1960) 154-181.
  • [4] C. Lanczos, Boundary value problems and orthogonal expansions, SIAM J. Appl. Math. 14(4) (1966) 831-863.
  • [5] C. Lanczos, Linear differential operators, Dover, New York (1997).
  • [6] G. H. Golub, Aspects of scientific computing, Johann Bernoulli Lecture, University of Groningen, 8th April 1996.
  • [7] Ch. L. Lawson, R. J. Hanson, Solving least squares, SIAM, Philadelphia, USA (1987).
  • [8] E. H. Moore, On the reciprocal of the general algebraic matrix, Bull. Amer. Math. Soc. 26(9) (1920) 394-395.
  • [9] A. Bjerhammar, Rectangular reciprocal matrices, with special reference to geodetic calculations, Bull. Géodésique (1951) 188-220.
  • [10] R. Penrose, A generalized inverse for matrices, Proc. Camb. Phil. Soc. 51 (1955) 406-413.
  • [11] M. Zuhair Nashed (Ed.), Generalized inverses and applications, Academic Press, New York (1976).
  • [12] A. Ben-Israel, The Moore of the Moore-Penrose inverse, Electron. J. Linear Algebra 9 (2002) 150-157.
  • [13] A. Ben-Israel, T. N. E. Greville, Generalized inverses: Theory and applications, Springer-Verlag, New York (2003).
  • [14] H. Schwerdtfeger, Direct proof of Lanczos decomposition theorem, Amer. Math. Monthly 67(9) (1960) 855-860.
  • [15] G. W. Stewart, On the early history of the SVD, SIAM Rev. 35 (1993) 551-566.
  • [16] H. Yanai, K. Takeuchi, Y. Takane, Projection matrices, generalized inverse matrices, and singular value decomposition, Springer, New York (2011) Chap. 3.
  • [17] P. Lam-Estrada, J. López-Bonilla, R. López-Vázquez, M. R. Maldonado, Least squares method via linear algebra, The SciTech, J. of Sci. & Tech. 2(2) (2013) 12-16.
  • [18] C. Lanczos, Applied analysis, Dover, New York (1988).
  • [19] R. Penrose, On the best approximate solutions of linear matrix equations, Proc. Camb. Phil. Soc. 52(1) (1956) 17-19.
  • [20] T. N. E. Greville, The pseudoinverse of a rectangular singular matrix and its application to the solution of systems of linear equations, SIAM Rev. 1(1) (1960) 38-43.
  • [21] J. Z. Hearon, Generalized inverses and solutions of linear systems, J. Res. Nat. Bur. Stand. B 72(4) (1968) 303-308.
  • [22] R. Tewarson, On minimax solutions of linear equations, The Computer Journal 15(3) (2018) 277-279.
Document Type
short_communication
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.psjd-03f386e5-1be3-4ae0-8cad-2297a0898851
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