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--ZusammenfassungOn Global Convergence of Coordinate Relaxation in the Case of an Unsymmetrical, Diagonally Dominant Jacobian. We prove some new theorems on global convergence for a general class of coordinate relaxation schemes to solve systems of nonlinear equations. Those systems are assumed to admit a sealing of the dependent or independent variables such that the arising Jacobian is column or row diagonally dominant, resp. We extend one of these theorems to the case of coordinate relaxation with projection to solve discrete obstacle problems, and give examples for the application. AMS Subject Classifications." 65H 10, 65N20.Key words'." Coordinate relaxation, global convergence, diagonal dominance, discrete obstacle problems, quasilinear elliptic equations.Globale Konvergenz yon Relaxationsverfahren bei unsymmetrischer, diagonaldominanter Funktionalmatrix. Es werden einige neue Konvergenzs~itze ftir eine allgemeine Klasse yon Koordinatenrelaxationen zur Lrsung nichtlinearer Gleichungssysteme bewiesen. Dabei wird die Existenz einer Skalierung der abhfingigen oder unabh/ingigen Variablen vorausgesetzt, so dab die entstehende Funktionalmatrix spalten-bzw. zeilendiagonaldominant ist. Einer dieser S~itze wird tibertragen auf die ,,Koordinatenrelaxation mit Projektion" zur L6sung diskretisierter Hindernisprobleme. Schlid3lich werden Beispiele zur Anwendbarkeit gegeben. O. IntroductionThough there are faster algorithms, relaxation methods still play an important role in solving large nonlinear systems with sparse Jacobian, especially in solving systems that arise as discrete analoga of nonlinear boundary and initial boundary value problems. One important reason therefor is the minimal storage requirement. another the most simple iteration scheme. May be for this reasons coordinate relaxation yet appears in modern methods such as preconditioned cg (see Concus, Golub, O'Leary [4] and others) or multigrid algorithms (see Brandt [2] and the literature cited there).Another advantage of relaxation methods is the "robustness" in view of the choice of the initial guess (that is: a large domain of convergence), compared for example to Newton's method and its numerous variants.

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