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Block-iterative methods for consistent and inconsistent linear equations. (English) Zbl 0416.65031

65F20 Numerical solutions to overdetermined systems, pseudoinverses
65F10 Iterative numerical methods for linear systems
15A09 Theory of matrix inversion and generalized inverses
Full Text: DOI EuDML
[1] Ben-Israel, A., Greville, T.N.E.: Generalized inverses, theory and applications. London: Wiley 1974 · Zbl 0305.15001
[2] Berman, A., Neumann, M.: Consistency and splittings. SIAM J. Numer. Anal.13, 877-888 (1976) · Zbl 0368.65023 · doi:10.1137/0713069
[3] Björck, Å.: Methods for sparse linear least squares problems. In: Sparse matrix computations, J.R. Bunch, D.J. Rose (eds.), pp. 177-199. London: Academic Press 1976 · Zbl 0351.65004
[4] Björck, Å., Elfving, T.: Accelerated projection methods for computing pseudoinverse solutions of systems of linear equations. BIT19, 145-163 (1979) · Zbl 0409.65022 · doi:10.1007/BF01930845
[5] Björck, Å., Golub, G.H.: Numerical methods for computing angles between linear subspaces. Math. Comput.27, 579-594 (1973) · Zbl 0282.65031
[6] Dyer, J.: Acceleration of the convergence of the Kaczmarz method and iterated homogenous transformations. Ph.D. thesis, Univ. of California, Los Angeles (1965)
[7] Elfving, T.: On some methods for entropy maximization and matrix scaling. Linköping (1979) Linear Algebra and Appl. (in press, 1980) · Zbl 0458.65052
[8] Gordon, R., Hermann, G.T.: Three-dimensional reconstruction from projections, a review of algorithms. Int. Rev. Cytol.38, 111-151 (1974) · doi:10.1016/S0074-7696(08)60925-0
[9] Gubin, L.G., Polyak, B.T., Raik, E.V.: The method of projections for finding the common point of convex sets. USSR Comp. Math. and Math. Phys.7, 1-24 (1967) · Zbl 0199.51002 · doi:10.1016/0041-5553(67)90113-9
[10] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Comput. Biol. Med.6, 273-294 (1976) · doi:10.1016/0010-4825(76)90066-4
[11] Householder, A.S.: The theory of matrices in numerical analysis. London: Blaisdell 1965 · Zbl 0161.03001
[12] Kaczmarz, S.: Angenäherte Auflösung von Systemen linearer Gleichungen. Bull. Internat. Acad. Polon. Sci. Cl.A., 335-357 (1937) · Zbl 0017.31703
[13] Kahan, W.: Gauss-Seidel methods of solving large systems of linear equations. Ph.D. thesis, Uv. of Toronto (1958)
[14] Keller, H.B.: On the solution of singular and semidefinite linear systems by iterations. SIAM J. Numer. Anal.2, 281-290 (1965) · Zbl 0135.37503
[15] Kydes, A.S., Tewarson, R.P.: An iterative method for solving partitioned linear equations. Computing15, 357-363 (1975) · Zbl 0331.65023 · doi:10.1007/BF02260319
[16] Meyer Jr., C.D., Plemmons, R.J.: Convergent powers of a matrix with applications to iterative methods for singular linear systems. SIAM J. Numer. Anal.14, 699-705 (1977) · Zbl 0366.65017 · doi:10.1137/0714047
[17] Nichols, N.K.: On the convergence of two-stage iterative processes for solving linear equations. SIAM J. Numer. Anal.,10, 460-469 (1973) · Zbl 0259.65040 · doi:10.1137/0710040
[18] Ortega, J.M., Rheinboldt, W.C.: Iterative solution of nonlinear equations in several variables. London: Academic Press 1970 · Zbl 0241.65046
[19] Peters, W.: Lösung linearen Gleichungssysteme durch Projection auf Schmitträume von Hyperebenen und Berechnung einer verallgemeinerten Inversen. Beiträge Numer. Math.5, 129-146 (1976) · Zbl 0359.65024
[20] Tanabe, K.: Projection method for solving a singular system of linear equations and its applications. Numer. Math.17, 203-214 (1971) · Zbl 0228.65032 · doi:10.1007/BF01436376
[21] Tanabe, K.: Characterization of linear stationary iterative processes for solving a singular system of linear equations. Numer. Math.22, 349-359 (1974) · Zbl 0312.65031 · doi:10.1007/BF01436918
[22] Tewarson, R.P.: Projection methods for solving sparse linear systems. Comput. J.12, 77-80 (1969) · Zbl 0164.46103
[23] Wainwright, R.L., Keller, R.F.: Algorithms for projection methods for solving linear systems of equations. Comput. Math. Appl.3, 235-245 (1977) · Zbl 0367.65017 · doi:10.1016/0898-1221(77)90098-0
[24] Whitney, T.M., Meany, R.K.: Two algorithms related to the method of steepest descent. SIAM J. Numer. Anal.4, 109-118 (1967) · Zbl 0173.17806 · doi:10.1137/0704010
[25] Wozniakowski, H.: Round-off error analysis of iterations for large linear systems. Report from Carnegie-Mellon Uv., Pittsburgh, Pennsylvania 15213 (1977) · Zbl 0425.65018
[26] Young, D.M.: Iterative solution of large linear systems. London: Academic Press 1971 · Zbl 0231.65034
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