. Directes, 85 A.1 La m ethode de Crout :::::::::::::::::: 85 A, La m ethode de Gauss, p.86

B. De-type-gradient-conjugu-e, 87 B.1 Introduction ::::::::::::::::::::::: 87 B.2 D eaenitions et classiaecation ::::::::::::::: 88 B.3 Le gradient conjugu epr econditionn e ::::::::: 91 B

. La-formule-de-Ëmonotonie, :, p.129

M. Bibliographie-micromagn-etisme and . Aid, Simulation de la r epartition en domaines des pi eces polaires des t^ etes d'enregistrement magn etique couches minces Magnetic domain walls in bubble materials, Th ese, Institut national Polytechnique de Grenoble INPGG, LMCèIMAG, LETIèCEA, 1979.

L. F. Zimmermann, T. A. Ashby, P. E. Manteuffel, and . Saylor, Nucl eation et stabilit e des lignes de Bloch dans les grenats ferrimagn etiques a anisotropie uniaxiale : Application aux m emoires a lignes de Bloch.T h ese, Universit edeParis-Sud, Centre d'Orsay A taxonomy for conjugate gradient methods, SIAM J. Numer. Anal, vol.27, pp.1542-1568, 1990.

P. G. Ciarlet, J. G. Ciarlet, D. P. Golub, and . Leary, Collection math ematiques appliqu ees pour la ma^ trise sous la direction de P A generalised conjugate gradient method for the numerical solution of elliptic 176 BIBLIOGRAPHIE partial diaeerential equations Academic press, Sparse Matrix Computations, pp.309-332, 1976.

V. Faber and T. Manteuffel, Necessary and Sufficient Conditions for the Existence of a Conjugate Gradient Method, SIAM Journal on Numerical Analysis, vol.21, issue.2, pp.352-362, 1984.
DOI : 10.1137/0721026

G. H. Golub and D. P. Leary, Some History of the Conjugate Gradient and Lanczos Algorithms: 1948???1976, SIAM Review, vol.31, issue.1, pp.31-50, 1989.
DOI : 10.1137/1031003

M. R. Hestenes and E. Stieffel, Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Standards, pp.49-409, 1952.

P. Joly, R esolution de syst emes lin eaires non sym etriques par des m ethodes de gradient conjugu e. Publications du Laboratoire d'analyse num erique 82045, 1982.

P. Joly, Analyse num erique matricielleavanc ee, 1988.

P. Joly, M ethodes de gradient conjugu e 2 polycopi ess, 1988.

P. Joly, M ethodes de gradient conjugu e pour r esoudre des syst emes lin eaires non sym etriques, Document MODULEF, vol.102, 1988.

F. G. Lou and A. Sameh, An expansion method for solving saddleípoint problems, 1993.

C. C. Paige and M. A. Saunders, Solution of Sparse Indefinite Systems of Linear Equations, SIAM Journal on Numerical Analysis, vol.12, issue.4, pp.617-629, 1975.
DOI : 10.1137/0712047

Y. Saad and M. H. Schultz, GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems, SIAM Journal on Scientific and Statistical Computing, vol.7, issue.3
DOI : 10.1137/0907058

M. A. Saunders, Routines symmlq, 1989.

P. Sonneveld-nonsymmetric-linear-systems, . J. Siam, . Sci, . Stat, R. Comput et al., Analyse num erique matricielle appliqu ee a l'art de l'ing enieur Van Der Vorst Bi-cgstab : A fast and smoothly converging variant of bi-cg for the solution of nonsymmetric linear systems Singularit es ëBG80ë H Analycity of solutions of the OONN non-linear ç-model Harmonic maps with defects Harmonic mappings of Riemannian manifolds Hybrid method for computing demagnetizing aeelds The singular set of the minima of certain quadratic functionnals, ëDL85ë R. Dautray et J. L. Lions. Analyse Math ematique et Calcul Num erique pour les Sciences et Techniques, tome 2. Collection Commissariat a l'Energie Atomique, pp.36-52, 1964.

D. Gilbarg, N. S. Trudinger, S. Hildeberandt, H. Kaul, K. O. Widman et al., Elliptic partial diaeerential equations of seond order, second edition An existence theorem for harmonic mappings of Riemannian manifolds On the Hí older continuityofweak solutions of quasilinear elliptic systems of second order, Ural'Ceva. Equations aux d eriv ees partielles du type elliptique. Monographies universitaires de math ematiques, pp.550-569145, 1948.

C. B. Morrey, R. Schçn, and K. Uhlenbeck, Multiple integrals in the calculus of variations Die Grundlehren der matematischen Wissenschaften in Eingeldarstellungen A regularity theory for harmonic maps 17:307í335, 1982. ëSU83ë R. Schçn and K. Uhlenbeck. Boundary regularity and the Dirichlet problem for harmonic maps, ëSch61ë L. Schwartz. M ethodes Math ematiques pour les Sciences Physiques, pp.253-268, 1961.