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Projection method for solving a singular system of linear equations and its applications. (English) Zbl 0228.65032


MSC:

65F10 Iterative numerical methods for linear systems
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References:

[1] Forsythe, G. E.: Solving linear algebraic equations can be interesting. Bull. Amer. Math. Soc.59, 299-329 (1953). · Zbl 0050.34603
[2] Kaczmarz, S.: Angenäherte Auflösung von Systemen linearer Gleichungen. Bull. Acad. Polon. Sciences et Lettres, A, 355-357 (1937). · Zbl 0017.31703
[3] Nagasaka, H.: Error propagation in the solution of tridiagonal linear equations. Information Processing in Japan5, 38-44 (1965). · Zbl 0222.65040
[4] Penrose, R.: A generalized inverse for matrices. Proc. Cambr. Phil. Soc.51, 406-413, (1955). · Zbl 0065.24603
[5] Robinson, D.W.: On the generalized inverse of an arbitrary linear transformation. Amer. Math. Monthly69, 412-416 (1962). · Zbl 0106.01602
[6] Rosen, J. B.: The gradient projection method for nonlinear programming. Part II, nonlinear constraints. J. Soc. Indust. Appl. Math.9, no. 4 514-532 (1961). · Zbl 0231.90048
[7] Tanabe, K.: An algorithm for the constrained maximization in nonlinear programming, Research Memorandum No. 31, The Institute of Statistical Mathematics, 1969.
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