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Stoyan, G.

On a maximum principle for matrices, and on conservation of monotonicity. With applications to discretization methods. (English) Zbl 0501.65011

Z. Angew. Math. Mech. 62, 375-381 (1982).
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Cited in 1 Review
Cited in 12 Documents

MSC:

65F10 Iterative numerical methods for linear systems
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
15B48 Positive matrices and their generalizations; cones of matrices

Keywords:

monotonicity properties; maximum principle; matrices of monotone kind; monotonicity of the solution; difference schemes
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\textit{G. Stoyan}, Z. Angew. Math. Mech. 62, 375--381 (1982; Zbl 0501.65011)
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References:

[1] [Russian Text Ignored.] 1977.
[2] ; , An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs 1973.
[3] Collatz, Arch. der Math. 3 pp 365– (1952)
[4] Funktionalanalysis und Numerische Mathematik, Springer, Berlin 1964.
[5] Schröder, Arch. Rat. Mech. Analysis 8 pp 408– (1961)
[6] Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs 1962. · Zbl 0133.08602
[7] ; , Iterative Solution of Nonlinear Equations in Several Variables, Acad. Press, N.Y. 1970.
[8] Monotonie: Lösbarkeit und Numerik bei Operatorgleichungen, Springer, Berlin 1974. · Zbl 0281.47032
[9] Varga, SIAM J. Numer. Analysis 3 pp 355– (1966)
[10] Ciarlét, Aequationes math. 4 pp 338– (1970)
[11] Stieltjes, Acta Math. 9 pp 385– (1887)
[12] Lorenz, Numer. Math. 27 pp 227– (1977)
[13] [Russian Text Ignored.]
[14] [Russian Text Ignored.]
[15] [Russian Text Ignored.]
[16] Birkhoff, Ser. A 5 pp 147– (1946)
[17] Banach Lattices and Positive Operators, Springer, Berlin 1974. · Zbl 0296.47023
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