Publications

    This page contains LINKS for downloading preprints and software.

    Contents:

    Books:

    1. Allgower, E. L. & Georg, K.: Numerical path following. In P. G. Ciarlet and J. L. Lions, editors,  Handbook of Numerical Analysis, volume 5, North-Holland (1997) 3-207. Download the file AllgGeorgHNA.ps.Z (2117K) or AllgGeorgHNA.pdf (1044K)
    2. Allgower, E. L. & Georg, K.: Numerical continuation methods: An Introduction. Series in Computational Mathematics 13, Springer Verlag, Heidelberg, 1990, pp 388. The book is out of print, but will appear in the SIAM Classics in Applied Mathematics Series. You can also download the file book_programs.txt (73K) which contains the FORTRAN programs of this book
    3. Allgower, E. L. & Georg, K. & Miranda, R. (eds.): Exploiting Symmetry in Applied and Numerical Analysis. Lectures in Applied Mathematics Series 28, American Mathematical Society, Providence, 1993.
    4. Allgower, E. L. & Georg, K. (eds.): Computational solution of nonlinear systems of equations. Lectures in Applied Mathematics Series 26, American Mathematical Society, Providence, 1990, pp 776.

    Other Publications:

    1. Georg, K.: A New Exclusion Test, to appear in Journal of Computational and Applied Mathematics (2002). Download the file lp_excl_1.pdf (211K)
    2. Allgower, E. L. & Erdmann, M. & Georg, K.: On the Complexity of Exclusion Algorithms for Optimization, Journal of Complexity, vol. 18, no. 2 (2002), 573-588. Download the file opt_excl_1.pdf (157K)
    3. Georg, K.: Improving the Efficiency of Exclusion Algorithms, Advances in Geometry, vol. 1 (2001), 193-210. Download the file cell_excl_3.pdf (157K)
    4. Georg, K.: Matrix-Free Numerical Continuation and Bifurcation, Numerical Functional Analysis and Optimization, vol. 22 (2001), 303-320. Download the file MatrixFree.ps.Z (549K) or MatrixFree.pdf (223K)
    5. Allgower, E. L. & Georg, K.: Piecewise Linear Methods for Nonlinear Equations and Optimization, Journal of Computational and Applied Mathematics, volume 124, Special Issue on Numerical Analysis 2000: Vol. IV: Optimization and Nonlinear Equations, 2000. Download the file NEO.ps.Z (150K) or NEO.pdf (209K) or NEO.tex
    6. Allgower, E. L. & Georg, K.: Exploiting Symmetry in Numerical Solving, in: Proceedings of the Seventh Workshop on Differential Equations and its Applications, C.-S. Chien, editor, Taichung, Taiwan, to appear. Download the file taiwan.ps.Z (142K) or taiwan.pdf (204K)
    7. Allgower, E. L. & Georg, K.: Numerical Exploitation of Symmetric Structures in BEM, Computational Engineering, vol 1, Golberg, M., editor, Computational Mechanics Publications, Southampton (1998) 289-306. Download the file golberg.ps.Z (197K) or golberg.pdf (193K)
    8. Allgower, E. L. & Georg, K.: Numerical Exploitation of Symmetry in Integral Equation, Advances in Computational Mathematics, vol 9, (1998) 1-20. Download the file IntEqPaper.ps.Z (165K) or IntEqPaper.pdf (224K)
    9. Allgower, E. L. & Georg, K.: Exploiting Symmetry in BEM, in: Boundary Element Technology XII, Frankel, J. I., Brebbia, C. A., Aliabadi, M. A. H., editors, Computational Mechanics Publications, (1997) 429--448. Download the file betech97.ps.Z (177K) or betech97.pdf (197K)
    10. Allgower, E. L. & Georg, K. & Miranda, R. & Tausch, J.: Equivariance and Fixed Points, ZAMM, vol 78 (1998) 795-806. Download the file AGMTzamm.ps.Z (124K) or AGMTzamm.pdf (217K)
    11. Georg, K. & Tausch, J.: User's Guide for a Package to Solve Equivariant Linear Systems, Manual, Colorado State University (1995). Download the file GFTpack.tar.Z (964K) which contains the manual and a software package
    12. Georg, K. & Tausch, J.: Some error estimates for the numerical approximation of surface integrals. Math. Comp., (1994), 755-763. Download the file SurfEstimPaper.ps.Z (54K) or SurfEstimPaper.pdf (131K)
    13. Georg, K. & Tausch, J.: A generalized Fourier Transform for boundary element methods with symmetries. Preprint (1994). Download the file or fipos.pdf (232K)
    14. Allgower, E. L. & Georg, K. & Miranda, R.: Exploiting permutation symmetry with fixed points in linear equations. In: Exploiting Symmetry in Applied and Numerical Analysis, E. L. Allgower, K. Georg, and R. Miranda, editors, Lectures in Applied Mathematics 29, American Mathematical Society (1993), 23-36. Download the file WithFPpaper.ps.Z (66K) or WithFPpaper.pdf (176K)
    15. Allgower, E. L. & Georg, K. & Walker, J.: Exploiting symmetry in 3D boundary element methods. In: Contributions in Numerical Mathematics, R. P. Agarwal, editor, World Scientific Series in Applicable Analysis 2, World Scientific Publ. Comp., Singapore (1993), 15-25. Download the file singapore.pdf (123K)
    16. Allgower, E. L. & Georg, K.: Continuation and path following. Acta Numerica 2, (1993), 1-64. Download the file actapaper.ps.Z (195K) or actapaper.pdf (443K)
    17. Georg, K. & Widmann, R.: Adaptive quadrature over surfaces. Preprint (1993). Download the file adquadsurf.pdf (170K)
    18. Georg, K. & Miranda, R.: Exploiting symmetry in solving linear equations. In: Bifurcation and symmetry: Cross influences between mathematics and applications, E. L. Allgower and K. Böhmer and M. Golubitsky, editors, ISNM 104, Birkhäuser Verlag (1992), 157-168. Download the file marburg.pdf (125K)
    19. Georg, K. & Widmann, R.: Adaptive quadratures over volumes. Computing 47, 121-136 (1991). Download the file AdapQuadVol.pdf (179K). Look also at the file ralf.tar.Z (66K) which contains two preprints (in LaTeX source code) and three C-programs of Ralf Widmann concerning efficient and automatic triangulations of surfaces and volumes
    20. Allgower, E. L. & Georg, K. & Kalik, K.: Computation of weakly and nearly singular integrals over triangles in R3 . Univ. u Novom Sadu, Zb. Rad. Prirod.-Mat. Fak., Ser. Mat. 22, 149-158 (1992). Download the file CompIntTriang.pdf (129K)
    21. Allgower, E. L. & Georg, K. & Widmann, R.: Volume integrals for boundary element methods. J. Comput. Appl. Math. 38, 17-29 (1991). Download the file volintBEM.pdf (137K). Also download the file ralf.tar.Z (66K) which contains two preprints (in LaTeX source code) and three C-programs of Ralf Widmann concerning efficient and automatic triangulations of surfaces and volumes
    22. Allgower, E. L. & Georg, K. & Miranda, R.: The method of resultants for computing real solutions of polynomial systems. SIAM J. Numer. Anal. 29 (1992). Download the file resultant.pdf (174K)
    23. Allgower, E. L. & Böhmer, K. & Georg, K. & Miranda, R.: Exploiting symmetry in boundary element methods. SIAM J. Numer. Anal. 29, 534-522 (1992). Download the file ABGMsym.pdf (218K)
    24. Allgower, E. L. & Chien, C.-S. & Georg, K. & Wang, C.-F.: Conjugate gradient methods for continuation problems. J. Comput. Appl. Math. 38, 1-16 (1991).
    25. Georg, K.: Approximation of integrals for boundary element methods. SIAM J. Sci. Stat. Comput. 12, 443-453, (1991). Download the file ApproxIntBEM.pdf (175K)
    26. Georg, K. & Zachmann, D.: Nonlinear convection diffusion equations and Newton-like methods. In: Computational solution of nonlinear systems of equations, Lectures in Applied Mathematics 26, 237-256, E. L. Allgower & K. Georg, editors, American Mathematical Society, (1990).
    27. Allgower, E. L. & Georg, K.: Estimates for piecewise linear approximations of implicitly defined manifolds. Appl. Math. Lett. 1.5, 1-7, (1989). Download the file estPLman.pdf (102K)
    28. Georg, K.: An introduction to PL algorithms. In: Computational solution of nonlinear systems of equations, Lectures in Applied Mathematics 26, 207-236, E. L. Allgower & K. Georg, editors, American Mathematical Society, (1990). Download the file PLintro.pdf (247K)
    29. Allgower, E. L & Chien, C.-S. & Georg, K.: Large sparse continuation problems. Journal of Computational and Applied Mathematics 26, 1-19, (1989).
    30. Allgower, E. L. & Georg, K.: Numerically stable homotopy methods without an extra dimension. In: Computational solution of nonlinear systems of equations, Lectures in Applied Mathematics 26, 1-13, E. L. Allgower & K. Georg, editors, American Mathematical Society, (1990). Download the file homExtra.pdf (148K)
    31. Georg, K. & Hettich, R.: On the numberical stability of simplex algorithms. Optimization 18, 361-372, (1987).
    32. Allgower, E. L. & Georg, K.: Predictor-corrector and simplicial methods for approximating fixed pints and zero points of nonlinear mappings. In: Mathematical programming: The state of the art. A. B. Nachem & M. Grotschel & B. Korte, editors. Springer Verlag, Berlin, Heidelberg, New York, (1983).
    33. Allgower, E. L. & Georg, K.: Relationships between deflation and global methods in the problem of approximating additional zeroes of a system of nonlinear equations. In: Homotopy methods and global convergence. B. C. Eaves & F. G. Gould & H.-O. Peitgen & M. J. Todd, editors, Plenum Press, New York, 31-42, (1983)
    34. Georg, K.: A note on stepsize control for numerical curve following. In: Homotopy methods and global convergence. B. C. Eaves & F. J. Gould & H.-O. Peitgen & M. J. Todd, editors. Plenum Press, New York, 145-154, (1983).
    35. Georg, K.: Zur numerischen Realisierung von Kontinuitatmethoden mit Pradiktor-Korrektor-oder simplizialen Verfahren. Habilitationsschrift, Univ. Bonn, Germany, (1982).
    36. Georg, K.: On tracing an implicitly defined curve by quasi-Newton steps and calculating bifurcation by local perturbation. SIAM J. Sci. Stat. Comput. 2, 35-50, (1981).
    37. Georg, K.: A numerically stable update for simplicial algorithms. In: Numerical solution of nonlinear equations. E. Allgower & K. Glashoff & H.-P. Peitgen, editors. Lecture Notes in Math. 878, 117-127, (1981).
    38. Georg, K.: Numerical integration of the Davidenko equation. In: Numerical solution of nonlinear equations. E. Allgower & K. Glashoff & H.-O. Peitgen, editors. Lecture Notes in Math. 878, 117-127, (1981).
    39. Allgower, E. L. & Georg, K.: Homotopy methods for approximating several solutions to nonlinear systems of equations. In: Numerical solutions of highly nonlinear problems. W. Forster, editor. North-Holland, Amsterdam, New York, 253-270, (1980).
    40. Allgower, E. L. & Georg, K.: Simplicial and continuation methods for approximating fixed points and solutions to systems of equations. SIAM Review 22, 28-85, (1980).
    41. Georg, K.: A simplicial deformation algorithm with applications to optimization, variational inequalities and boundary value problems. In: Numerical solution of highly nonlinear problems. W. Forster, editor, North-Holland, Amsterdam, New York, 361-375, (1980).
    42. Allgower, E. L. & Georg, K.: Generation of triangulations by reflections. Utilitas Math. 16, 123-129, (1979).
    43. Georg, K.: An iteration method for solving nonlinear eigenvalue problems. In: Constructive methods for nonlinear boundary value problems and nonlinear oscillations. J. Albrecht & L. Collatz & K.Kirchgässner, editors, ISNM 48, Birkhouser Verlag, 38-47, (1979).
    44. Georg, K.: On the convergence of an inverse iteration method for nonlinear elliptic eigenvalue problems. Numer. Math. 32, 69-74, (1979).
    45. Georg, K.: An application of simplicial algorithms to variational inequalities. In: Functional differential equations and approximation of fixed points. H. -O. Peitgen & H. -O Walther, editors. Lecture Notes in Math. 730, 126-135, (1979).
    46. Georg, K.: Algoritmi simpliciali come realizzazione numerica del grado di Brouwer. In: A survey on the theoretical and numerical trends in nonlinear analysis. Gius. Laterza & Figi, Bari, 60-120, (1979).
    47. Allgower, E. L. & Georg, K.: Triangulations by reflections with applications to approximation. In:Numerische Methoden der Approximationstheorie. L.Collatz & G. Meinardus & H.Werner, editors ISNM 42. Birkhäuser Verlag, Basel, 10-32, (1978).
    48. Georg, K.: On the convergence of an inverse iteration method for nonlinear boundary value problems. In: Equazioni differenziali ordinarie ed equazioni funzionali. R. Conti & G. Sestini & G. Villari, editors. CNR, Florence, 317-321, (1978).
    49. Georg, K. & Martelli, M.: On spectral theory for nonlinear operators. J. Func. Anal. 14, 140-140, (1977).
    50. Georg, K.: On surjectivity of quasi bounded alpha-Lipschitz maps. Bollettino UMI (5), 13-A, 117-122, (1976).

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