Conjugate gradient methods for continuation problems II

[1]  W. Arnoldi.  The principle of minimized iterations in the solution of the matrix eigenvalue problem , 1951 .

[2]  H. Keller,et al.  Analysis of Numerical Methods , 1969 .

[3]  E. Polak,et al.  Note sur la convergence de méthodes de directions conjuguées , 1969 .

[4]  Edward L. Reiss,et al.  Block five diagonal matrices and the fast numerical solution of the biharmonic equation , 1972 .

[5]  J. Meijerink,et al.  An iterative solution method for linear systems of which the coefficient matrix is a symmetric -matrix , 1977 .

[6]  W. Rheinboldt.  Numerical methods for a class of nite dimensional bifur-cation problems , 1978 .

[7]  W. Rheinboldt.  Numerical analysis of continuation methods for nonlinear structural problems , 1981 .

[8]  Y. Saad.  Krylov subspace methods for solving large unsymmetric linear systems , 1981 .

[9]  K. Georg.  On Tracing an Implicitly Defined Curve by Quasi-Newton Steps and Calculating Bifurcation by Local Perturbations , 1981 .

[10]  Y. Saad.  The Lanczos Biorthogonalization Algorithm and Other Oblique Projection Methods for Solving Large Unsymmetric Systems , 1982 .

[11]  Josef Stoer,et al.  Solution of Large Linear Systems of Equations by Conjugate Gradient Type Methods , 1982, ISMP.

[12]  K. Georg.  A Note on Stepsize Control for Numerical Curve Following , 1983 .

[13]  Gene H. Golub,et al.  Matrix computations , 1983 .

[14]  H. Schwetlick.  On the Choice of Steplength in Path Following Methods , 1984 .

[15]  T. Chan.  Deflation Techniques and Block-Elimination Algorithms for Solving Bordered Singular Systems , 1984 .

[16]  T. Chan,et al.  Iterative Methods for Solving Bordered Systems with Applications to Continuation Methods , 1985 .

[17]  H. Keller,et al.  Continuation-Conjugate Gradient Methods for the Least Squares Solution of Nonlinear Boundary Value Problems , 1985 .

[18]  H. Keller,et al.  A multigrid continuation method for elliptic problems with folds , 1986 .

[19]  T. Chan,et al.  PLTMGC: A Multigrid Continuation Program for Parameterized Nonlinear Elliptic Systems , 1986 .

[20]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[21]  W. Rheinboldt.  Numerical analysis of parametrized nonlinear equations , 1986 .

[22]  E. Allgower,et al.  Continuation and local perturbation for multiple bifurcations , 1986 .

[23]  Hans D Mittlemann.  A pseudo-arclength continuation method for nonlinear eigenvalue problems , 1986 .

[24]  H. Schwetlick,et al.  Higher order predictors and adaptive steplength control in path following algorithms , 1987 .

[25]  J. Dennis,et al.  Generalized conjugate directions , 1987 .

[26]  H. Walker.  Implementation of the GMRES method using householder transformations , 1988 .

[27]  H. V. D. Vorst,et al.  Conjugate gradient type methods and preconditioning , 1988 .

[28]  H. Keller.  Lectures on Numerical Methods in Bifurcation Problems , 1988 .

[29]  P. Sonneveld.  CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems , 1989 .

[30]  Y. Saad,et al.  Krylov Subspace Methods on Supercomputers , 1989 .

[31]  C.-S. Chien,et al.  Large sparse continuation problems , 1989 .

[32]  Jacques Huitfeldt,et al.  A New Algorithm for Numerical Path Following Applied to an Example from Hydrodynamical Flow , 1990, SIAM J. Sci. Comput..

[33]  Youcef Saad,et al.  A Basic Tool Kit for Sparse Matrix Computations , 1990 .

[34]  E. Allgower,et al.  A Complete Bifurcation Scenario for the 2-d Nonlinear Laplacian with Neumann Boundary Conditions on the Unit Square , 1991 .

[35]  Z. Mei,et al.  Path following around corank-2 bifurcation pints of a semi-linear elliptic problem with symmetry , 1991 .

[36]  Zhen Mei,et al.  Bifurcations of a simplified buckling problem and the effect of discretizations , 1991 .

[37]  R. Freund,et al.  QMR: a quasi-minimal residual method for non-Hermitian linear systems , 1991 .

[38]  Henk A. van der Vorst,et al.  Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems , 1992, SIAM J. Sci. Comput..

[39]  G. Golub,et al.  Iterative solution of linear systems , 1991, Acta Numerica.