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Nonnegative splitting theory. (English) Zbl 0805.65033
This paper generalizes the concept and the theory of the well-known regular splitting, when A=M-N and it is assumed that M -1 , M -1 N, and NM -1 are all nonnegative. Applications are given in comparing the convergence speeds of iteration methods for solving linear algebraic equations.

65F10Iterative methods for linear systems
15A48Positive matrices and their generalizations (MSC2000)
[1]R.S. Varga, Matrix Iterative Analysis. Prentice Hall, Englewood Cliffs, N.J., 1962.
[2]Z.I. Woźnicki, Two-sweep iterative methods for solving large linear systems and their application to the numerical solution of multi-group, multi-dimensional neutron diffusion equations. Doctoral, Dissertation, Rep. No. 1447-CYFRONET-PM-A, Inst. Nuclear Res., Swierk-Otwock, Poland, 1973.
[3]Z.I. Woźnicki, AGA two-sweep iterative method and their application in critical reactor calculations. Nukleonika,9 (1978), 941–968.
[4]Z.I. Woźnicki, AGA two-sweep iterative methods and their application for the solution of linear equation systems. Proc. International Conference on Linear Algebra and Applications., Valencia, Spain, Sept. 28–30, 1987 (published in Linear Algebra Appl.,121 (1989), 702–710.
[5]Z.I. Woźnicki, Estimation of the optimum relaxation factors in the partial factorization iterative methods. Proc. International Conference on the Physics of Reactors: Operation, Design and Computations, Marseille, France, April 23–27, 1990, pp. P-IV-173-186. (To appear at beginning 1993 in SIAM J. Matrix Anal. Appl.)
[6]J.M. Ortega and W. Rheinboldt, Monotone iterations for nonlinear equations with applications to Gauss-Seidel methods. SIAM J. Numer. Anal.,4 (1967), 171–190. · Zbl 0161.35401 · doi:10.1137/0704017
[7]G. Csordas and R.S. Varga, Comparison of regular splittings of matrices. Numer. Math.,44 (1984), 23–35. · Zbl 0556.65024 · doi:10.1007/BF01389752
[8]G. Alefeld and P. Volkmann, Regular splittings and monotone iteration functions. Numer. Math.,46 (1985), 213–228. · Zbl 0571.65043 · doi:10.1007/BF01390420
[9]V.A. Miller and M. Neumann, A note on comparison theorems for nonnegative matrices. Numer. Math.,47 (1985), 427–434. · Zbl 0557.65020 · doi:10.1007/BF01389590
[10]L. Elsner, Comparisons of weak regular splittings and multisplitting methods. Numer. Math.,56 (1989), 283–289. · Zbl 0673.65018 · doi:10.1007/BF01409790
[11]I. Marek and D.B. Szyld, Comparison theorems for weak splittings of bounded operators. Numer. Math.,58 (1990), 389–397. · Zbl 0694.65023 · doi:10.1007/BF01385632
[12]Z.I. Woźnicki, HEXAGA-II-120, 0, 0 Two-dimensional multi-group neutron diffusion programmes for a uniform triangular mesh with arbitrary group scattering. Report KfK-2789, 1979.
[13]Z.I. Woźnicki, HEXAGA-III-120, 0 Three-dimensional multi-group neutron diffusion programmes for a uniform triangular mesh with arbitrary group scattering. Report KfK-3572, 1983.
[14]Z.I. Woźnicki, Two- and three-dimensional benchmark calculations for triangular geometry by means of HEXAGA programmes. Proc. International Meeting on Advances in Nuclear Engineering Compuational Methods, Knoxville, Tennessee, April 9–11, 1985, pp. 147–156.
[15]R. Beauwens, Factorization iterative methods, M-operators and H-operators. Numer. Math.,31 (1979), 335–357. · Zbl 0431.65012 · doi:10.1007/BF01404565
[16]H.C. Elman and G.H. Golub, Line iterative methods for cyclically reduced discrete convection-diffusion problems. SIAM J. Sci. Statist. Comput.,13 (1992), 339–363. · Zbl 0752.65067 · doi:10.1137/0913018
[17]Z.I. Woźnicki, The graphic representation of the algorithims of the AGA two-sweep iterative method (under preparation).
[18]Z.I. Woźnicki, On numerical analysis of conjugate gradient method. Japan J. Indust. Appl. Math.,10 (1993), 487–519. · Zbl 0802.65037 · doi:10.1007/BF03167286
[19]Z.I. Woźnicki, The Sigma-SOR algorithm and the optimal strategy for the utilization of the SOR iterative method. Math. Comp.,62 206 (1994), 619–644. · Zbl 0802.65036 · doi:10.2307/2153527