Alternating Direction Implicit Methods

Birkhoff, 1959, Implicit alternating direction methods, Trans. AMS, 92, 13, 10.1090/S0002-9947-1959-0105814-4 Bruce, 1953, Calculation of unsteady-state gas flow through porous media, Trans. AIMME, 198, 79 Conte, 1958, An alternating direction scheme for the biharmonic difference equations, Math. Tables Aid Computing., 12, 198, 10.2307/2002021 de Boor C. M.J.R. Rice, Tchebycheff approximation by αII[(x −rj)(x +rj)] and application to ADI iteration. To appear in J. Soc. Ind. AppL. Math. Douglas, 1957, A note on the alternating direction implcitcit method for the numerical solution of heat flow problems, Proc. AMS, 8, 409, 10.1090/S0002-9939-1957-0090876-7 Douglas, 1955, On the numerical integration of σ2u/σx2 + σ2u/σy2 = σu/σt by implicit methods, J. Soc. Ind. Appl. Math., 3, 42, 10.1137/0103004 Douglas, 1961, Alternating direction iteration for mildly nonlinear elliptic differential equations, Numerical. Math., 3, 92, 10.1007/BF01386006 Douglas, 1956, On the numerical solution of heat conduction problems in two and three space variables, Trans. AMS, 82, 421, 10.1090/S0002-9947-1956-0084194-4 Forsythe, 1960 Fort, 1948 Frankel, 1950, Convergence rates of iterative treatments of partial differential equations, Math. Tables Aid Comput., 4, 65, 10.2307/2002770 Gantmakher, 1937, Sur les matrices completement non-negatives et oscillatoires, Compositio Math., 4, 445 Golub, 1961, Chebyshev semi-iterative methods, successive overrelaxation iterative methods, and second order Richardson iterative methods, I, Numer. Math., 3, 147, 10.1007/BF01386013 1962, Numer. Math., 3, 157 Heller, 1960, Simultaneous successive and alternating direction schemes, J. Soc. Ind. and Appl. Math., 8, 150, 10.1137/0108009 Householder, 1958, The approximate solution of matrix problems, J. Assoc. Computing Machinery, 5, 205, 10.1145/320932.320933 Kryloff, 1931, Les méthodes de solution approchée des problèmes de la physique mathématique, Mém. Sci. Math., 68 Lees, 1962, Alternating direction and semi-explicit difference methods for parabolic partial differential equations, Numer. Math., 3, 398, 10.1007/BF01386038 Ostrowski, 1954, On the linear iterative procedures for symmetric matrices, Rend. mat. appl. [5], 14, 140 appl, 1961, “Multi-line” iterative methods for elliptic difference equations and fundamental frequencies, Numer. Math., 3, 305, 10.1007/BF01386031 Peaceman, 1955, The numerical solution of parabolic and elliptic differential equations, J. Soc. Ind. and Appl. Math., 3, 28, 10.1137/0103003 Remes, 1934, Sur un procédé convergent d'approximations successives pour déterminer les polynomes d'approximation, Compt. rend. acad. sci., 19, 2063 1934, Sur le calcul effectif des polynomes d'approximation de Tchebichef, Compt. rend. acad. sci., 199, 337 Rice, 1961, Tchebycheff approximations by functions unisolvent of variable degree, Trans. AMS, 99, 298, 10.1090/S0002-9947-1961-0136913-8 Shortley, 1950, J. Appl. Phys., 21, 1326, 10.1063/1.1699598 Stiefel, 1959, Numerical methods of Tchebycheff approximation, 217 Thrall, 1957 R.S. Varga, Overrelaxation applied to implicit alternating direction methods. Proc. Intern. Congr. on Information Processing, Paris, pp. 85–90, June (1958) Varga, 1959, P-cyclic matrices: A generalization of the Young-Frankel successive overrelaxation scheme, Pacific J. Math., 9, 617, 10.2140/pjm.1959.9.617 Varga, 1962 Varga, 1960, Factorization and normalized iterative methods Varga, 1959, Orderings of the successive overrelaxation scheme, Pacific J. Math., 9, 925, 10.2140/pjm.1959.9.925 Varga, 1961, Higher order stable implicit methods for solving parabolic partial differential equations. J, Math. and Phys., 40, 220, 10.1002/sapm1961401220 Wachspress, 1957 Wachspress, 1960, An alternating-direction-implicit iteration technique, J. Soc. Ind. and Appl. Math., 8, 403, 10.1137/0108027 Wachspress, 1962, Optimum alternating-direction-implicit iteration parameters for a model problem, J. Soc. Ind. and Appl. Math., 10, 339, 10.1137/0110025 Weyl, 1912, Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen, Math. Ann. (Leipzig), 71, 441, 10.1007/BF01456804 D. Young, Iterative methods for solving partial difference equations of elliptic type. Ph.D. Thesis, Harvard (1950) Young, 1954, Iterative methods for solving partial difference equations of elliptic type, Trans. AMS, 76, 92, 10.1090/S0002-9947-1954-0059635-7 Young, 1955, Ordvac solutions of the Dirichlet problem, J. Assoc. Computing Machinery, 2, 137, 10.1145/320802.320803 Young, 1956, On the solution of linear systems by iteration, AMS Symposium on Numer. Anal., 6, 10.1090/psapm/006/0081539 Young, 1960