Abstract
There are many iterative methods for solving a consistent singular system of linear equations [2, 3, 5, 6, 8, 10–13]. In this paper we characterize the class of all singular system of linear equations using generalized inverses.
Similar content being viewed by others
References
Afriat, S.N.: Orthogonal and oblique projectors and the characteristics of pairs of vector spaces. Proc. Cambridge Philosophi. Soc.53, 800–816 (1957)
Douglas, J., Jr., Pearcy, C. M.: On convergence of alternating direction procedures in the presence of singular operators. Numer. Math.5, 175–184 (1963)
Joshi, V. N.: A note on the solution of rectangular linear systems by iteration. SIAM Review12, 463–466 (1970)
Forsythe, G. E., Moler, C. B.: Computer solution of linear algebraic systems. Prentice-Hall (1967)
Keller, H. B.: On the solution of singular and semidefinite linear systems by iteration. J. SIAM Numer. Anal. B-2, 289–290 (1965)
Pavel-Parvu, M., Korganoff, A.: Iteration functions for solving polynomial matrix equations. Constructive aspects of the fundamental theorem of algebra. (eds. Dejon, B., Henrici, P.) London: Wiley (1969)
Oldenburger, R.: Infinite powers of matrices and characteristic roots. Duke Math. J.6, 357–361 (1940)
Pyle, L. D.: A generalized inverseε-algorithm for constructing intersection projection matrices, with applications. Numer. Math.10, 86–102 (1967)
Rao, C. R., Mitra, S. K.: Generalized inverse of matrices and its applications. New York: Wiley 1971
Tanabe, K.: Projection method for solving a singular system of linear equations and its applications. Numer. Math.17, 203–214 (1971)
Tewarson, R. P.: On some representations of generalized inverses, SIAM Rev.11, 272–276 (1969)
Whitney, T. M., Meany, R. K.: Two algorithms related to the method of steepest descent. J. SIAM Numer. Anal.4, 109–118 (1967)
Young, D. M.: On the consistency of linear stationary iterative methods. J. SIAM Numer. Anal.9, 89–96 (1972)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tanabe, K. Characterization of linear stationary iterative processes for solving a singular system of linear equations. Numer. Math. 22, 349–359 (1974). https://doi.org/10.1007/BF01436918
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01436918