[2] W. E. ARNOLDI, The principle of minimized iterations in the solution of the matrix eigenvalue problem, Quart. Appl. Math., 9 (1951), pp

Transcription

1 Bibliography [1] A. ALAVI, J. KOHANOFF, M. PARRINELLO, AND D. FRENKEL, Ab initio molecular dynamics with excited electrons, Phys. Rev. Lett., 73 (1994), pp [2] W. E. ARNOLDI, The principle of minimized iterations in the solution of the matrix eigenvalue problem, Quart. Appl. Math., 9 (1951), pp [3] A. J. C. BELIËN, Wave dynamics and heating of coronal magnetic flux tubes, Ph.D. thesis, Vrije Universiteit Amsterdam, The Netherlands, [4] P. E. BJØRSTAD AND O. B. WIDLUND, To overlap or not to overlap: a note on a domain decomposition method for elliptic problems, SIAM J. Sci. Comput., 10 (1989), pp [5] J. G. BLOM AND J. G. VERWER, VLUGR3: a vectorizable adaptive grid solver for PDEs in 3D. I. algorithmic aspects and applications, Appl. Numer. Math., 16 (1994), pp [6] E. BRAKKEE, Domain decomposition for the incompressible Navier-Stokes Equations, Ph.D. thesis, Technische Universiteit Delft, Delft, The Netherlands, [7] E. BRAKKEE, AND P. WILDERS, The influence of interface conditions on convergence of Krylov-Schwarz domain decomposition for the advection-diffusion equation, J. Sci. Comput., 12 (1997), pp [8] X.-C. CAI, W. D. GROPP, AND D. E. KEYES, A comparison of some domain decomposition and ILU preconditioned iterative methods for nonsymmetric elliptic problems, Num. Lin. Alg. Appl. 1 (1994), pp [9] X.-C. CAI, W. D. GROPP, D. E. KEYES, R. G. MELVIN, AND D. P. YOUNG, Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation, SIAM J. Sci. Comput., 19: , [10] X.-C. CAI, AND D. E. KEYES, Nonlinearly preconditioned inexact Newton algorithms, submitted to SIAM J. Sci. Comput. 131

2 Bibliography 132 [11] T. F. CHAN AND D. GOOVAERTS, On the relationship between overlapping and nonoverlapping domain decomposition methods, SIAM J. Matrix Anal. Appl., 13 (1992), pp [12] T. F. CHAN AND T. P. MATHEW, Domain decomposition algorithms, Acta Numerica (1994), pp [13] R. CHEN AND H. GUO, Benchmark calculations of bound states of HO 2 via basic Lanczos algorithm, Chem. Phys. Lett., 277 (1997), pp [14] M. CROUZEIX, B. PHILIPPE, AND M. SADKANE, The Davidson method, SIAM J. Sci. Comput., 15 (1994), pp [15] E. R. DAVIDSON, The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices, J. Comput. Phys., 17 (1975), pp [16] Q. DENG, An analysis for a nonoverlapping domain decomposition iterative procedure, SIAM J. Sci. Comput., 18 (1997), pp [17] J. DESCLOUX, J.-L. FATTEBERT, AND F. GYGI, Rayleigh quotient iteration, an old recipe for solving modern large-scale eigenvalue problems, Computers in Physics, 12 (1998), pp [18] E. DE STURLER AND D. R. FOKKEMA, Nested Krylov methods and preserving the orthogonality, N. Duane Melson, T. A. Manteuffel, and S. F. McCormick, editors, Sixth Copper Mountain Conference on Multigrid Methods, NASA Conference Publication 3224, Part 1 (1993), pp [19], E. DE STURLER, Truncation strategies for optimal Krylov subspace methods, SIAM J. Numer. Anal., 36 (1999), pp [20] H. A. DIJKSTRA, M. J. SCHMEITS, AND C. A. KATSMAN, Internal variability of the North Atlantic wind-driven ocean circulation, Surveys in Geophysics, 20 (1999), pp [21] I. S. DUFF, R. G. GRIMES, AND J. G. LEWIS, Users guide for the Harwell-Boeing sparse matrix collection, Technical Report TR/PA/92/86, CERFACS, Toulouse, France, Also RAL Technical Report RAL [22] J.-L. FATTEBERT, Une méthode numérique pour la résolution des problèmes aux valeurs propres liés au calcul de structure électronique moléculaire, Ph.D. thesis, Ecole Polytechnique Fédérale de Lausanne, France, [23] J. G. F. FRANCIS, The QR transformation, a unitary analogue to the LR transformation part 1, Comp. J., 4 (1961), pp [24] J. G. F. FRANCIS, The QR transformation part 2, Comp. J., 4 (1961), pp

3 133 Bibliography [25] D. R. FOKKEMA, G. L. G. SLEIJPEN, AND H. A. VAN DER VORST, Accelerated inexact Newton schemes for large systems of nonlinear equations, SIAM J. Sci. Comput., 19 (1998), pp [26] D. R. FOKKEMA, G. L. G. SLEIJPEN, AND H. A. VAN DER VORST, Jacobi- Davidson style QR and QZ algorithms for the reduction of matrix pencils, SIAM J. Sci. Comput., 20 (1999), pp [27] J. P. GOEDBLOED, Plasma-vacuum interface problems in magnetohydrodynamics, Physica 12D (1984), pp [28] A. HADJIDIMOS, D. NOUTSOS, AND M. TZOUMAS, Nonoverlapping domain decomposition: a linear algebra viewpoint, Math. Comput. Simulation, 51 (2000), pp [29] Z. JIA, AND G. W. STEWART, An analysis of the Rayleigh-Ritz method for approximating eigenspaces, Technical Report TR-99-24/TR-4015, Department of Computer Science, University of Maryland, USA, [30] W. KERNER, J. P. GOEDBLOED, G. T. A. HUYSMANS, S. POEDTS, AND E. SCHWARZ, CASTOR: normal-mode analysis of resistive MHD plasmas, J. Comp. Phys., 142 (1998), pp [31] C. LANCZOS, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, Journal of Research, Nat. Bur. Stand., 45 (1950), pp [32] G. LUBE, L. MÜLLER, AND F. C. OTTO, A non-overlapping domain decomposition method for the advection-diffusion problem, Computing, 64 (2000), pp [33] R. B. MORGAN AND D. S. SCOTT, Generalizations of Davidson s method for computing eigenvalues of sparse symmetric matrices, SIAM J. Sci. Stat. Comput.,7 (1986), pp [34] R. B. MORGAN, On restarting the Arnoldi method for large nonsymmetric eigenvalue problems, Math. Comp., 65 (1996), pp [35] C. B. MOLER AND G. W. STEWART, An algorithm for generalized matrix eigenvalue problems, SIAM J. Num. Anal., 10 (1973), pp [36] J. OLSEN, P. JØRGENSEN, AND J. SIMONS, Passing the one-billion limit in full configuration-interaction (FCI) calculations, Chem. Phys. Lett.,169 (1990), pp [37] B. N. PARLETT, The symmetric eigenvalue problem, Prentice-Hall, Englewood Cliffs, N.J., 1980.

4 Bibliography 134 [38] TH. ROTTNER, I. LENHARDT, G. ALEFELD, AND K. SCHWEIZERHOF, Nonlinear structural finite element analysis using the preconditioned Lanczos method on serial and parallel computers, BIT, 37 (1997), pp [39] A. RUHE, Rational Krylov, a practical algorithm for large sparse nonsymmetric matrix pencils, SIAM J. Sci. Comput., 19 (1998), pp [40] Y. SAAD, Numerical methods for large eigenvalue problems, Manchester University Press, Manchester, UK, [41] Y. SAAD AND M. H. SCHULTZ, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., 7 (1986), pp [42] M. SADKANE, Block-Arnoldi and Davidson methods for unsymmetric large eigenvalue problems, Numer. Math., 64 (1993), pp [43] H. A. SCHWARZ, Gesammelte Mathematische Abhandlungen, Vol. 2, pp , Springer, Berlin, First published in Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich, 15 (1870), pp [44] G. L. G. SLEIJPEN, A. G. L. BOOTEN, D. R. FOKKEMA, AND H. A. VAN DER VORST, Jacobi-Davidson type methods for generalized eigenproblems and polynomial eigenproblems, BIT, 36 (1996), pp [45] G. L. G. SLEIJPEN AND H. A. VAN DER VORST, The Jacobi-Davidson method for eigenvalue problems and its relation with accelerated inexact Newton scheme. in Iterative Methods in Linear Algebra II, S. D. Margenov, and P. S. Vassilevski, eds., IMACS Ann. Comput. Appl. Math., 3: , [46] G. L. G. SLEIJPEN AND H. A. VAN DER VORST, A Jacobi-Davidson iteration method for linear eigenvalue problems, SIAM J. Matrix Anal. Appl., 17 (1996), pp [47] G. L. G. SLEIJPEN, H. A. VAN DER VORST, AND E. MEIJERINK, Efficient expansion of subspaces in the Jacobi-Davidson method for standard and generalized eigenproblems, Electron. Trans. Numer. Anal. 7 (1998), pp [48] G. L. G. SLEIJPEN AND F. W. WUBS, Effective preconditioning techniques for eigenvalue problems, preprint no. 1117, Dep. Math., University Utrecht, [49] B. F. SMITH, P. E. BJØRSTAD, AND W. D. GROPP, Domain decomposition: parallel multilevel methods for elliptic partial differential equations, Cambridge University Press, [50] D. C. SORENSEN, Truncated QZ methods for large scale generalized eigenvalue problems, ETNA, 7 (1998), pp

5 135 Bibliography [51] D. C. SORENSEN AND C. YANG, A truncated RQ-iteration for large scale eigenvalue calculations, SIAM J. Matrix Anal. Appl., 19 (1998), pp [52] A. STATHOPOULOS, Y. SAAD, AND C. F. FISCHER, Robust preconditioning of large sparse symmetric eigenvalue problems, J. Comput. Appl. Math., 64 (1995), pp [53] A. STATHOPOULOS, Y. SAAD, AND K. WU, Dynamic thick restarting of the Davidson, and the implicitly restarted Arnoldi methods, SIAM J. Sci. Comput., 19 (1998), pp [54] H. SUN AND W. P. TANG, An overdetermined Schwarz alternating method, SIAM J. Sci. Stat. Comput. 17 (1996), pp [55] K. H. TAN AND M. J. A. BORSBOOM, On generalized Schwarz coupling applied to advection-dominated problems, in Domain decomposition methods in scientific and engineering computing (University Park, PA, 1993), D. E. Keyes and J. C. Xu, eds., Amer. Math. Soc., Providence, RI, 1994, pp [56] K. H. TAN, Local coupling in domain decomposition, Ph.D. thesis, Utrecht University, Utrecht, The Netherlands, [57] W. P. TANG, Generalized Schwarz splittings, SIAM J. Sci. Stat. Comput., 13 (1992), pp [58] R. S. VARGA, Matrix iterative analysis, Prentice-Hall Inc., Englewood Cliffs, N.J., [59] H. A. VAN DER VORST AND C. VUIK, GMRESR: a family of nested GMRES methods, Num. Lin. Alg. Appl., 1 (1994), pp [60] C. VUIK, A. SEGAL, AND J. A. MEIJERINK, An efficient preconditioned CG method for the solution of a class of layered problems with extreme contrasts in the coefficients, J. Comput. Phys., 152 (1999), pp [61] P. WILDERS AND E. BRAKKEE, Schwarz and Schur: an algebraic note on equivalence properties, SIAM J. Sci. Comput., 20 (1999), pp [62] S. M. WILKINSON AND D. P. THAMBIRATNAM, Mode coupling in the vibration response of asymmetric buildings, Computers & Structures, 56 (1995), pp [63] J. XU, Iterative methods by space decomposition and subspace correction, SIAM Review, 34 (1992), pp [64] G. YAO AND R. E. WYATT, A Krylov-subspace Chebyshev method and its application to pulsed laser-molecule interaction, Chem. Phys. Lett., 239 (1995), pp

6